# Probability Review Solutions

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Probability Review Solutions. A family has three children. Using b to stand for and g to stand for, and using ordered triples such as bbg, find the following. a. draw a tree diagram to determine the sample space b. write the event E that the family has exactly two s c. write the event F that the family has at least two s d. write the event G that the family has three s e. p(e) f. p(f) g. p(g) h the probability that there are exactly two s given that the first child is a. a. Reading from the beginning to the end of each limb, we have the sample space of {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. b. This is asking for the elements in the sample space that have exactly two bs listed. These are {bbg, bgb, gbb}. c. This is asking for the elements of the sample space that have twp or more s. In other words, this is asking for those elements that have exactly two bs and those that have three bs. These are {gbb, bgb, bbg, bbb}. d. This is asking for the elements of the sample space that have three s. In other words, this is asking for those elements that have three bs. This is {bbb}.

2 e. For this problem, we need to divide the number of things in the event E (exactly two s) by the number of things in the sample space to find the probability the family will have exactly two s. This will 3 totalnumber of things in E give us p (E ) = = 8 totalnumber of things in the sample space f. For this problem, we need to divide the number of things in the event F (at least two s) by the number of things in the sample space to find the probability the family will have at least two s. This will 4 totalnumber of thingsin F give us p (F ) = = 8 totalnumber of thingsin the sample space g. For this problem, we need to divide the number of things in the event G (three s) by the number of things in the sample space to find the probability the family will have three s. This will give us p (G ) = 8 = totalnumber of thingsin G totalnumber of things in the sample space h. For this problem, we once again want to look at a tree diagram. Since we are asked to determine the probability that there are exactly two s given that the first child is a, we need to only look at the part of the tree diagram where the first child is a give.

3 We then find all the branches off a first that have exactly two s (this is circled in red). To find the probability of this, we multiply the probabilities of each piece as we work our way out starting with the probability after the first. This gives us = 4. Mendel found that snapdragons have no color dominance; a snapdragon with one red gene and one white gene will have pink flowers. If a pure red snapdragon is crossed with a pink snapdragon, find the following probabilities. a. a red offspring b. a white offspring c. a pink offspring The easiest way to do this problem is to use a Punnet square. The pure red snapdragon will have two red genes (represented by R in the Punnet square). The pink snapdragon will have one red (R) and one white (represented by W in the Punnet square). Red Snapdragon R R Pink Snapdragon R RR RR W RW RW a. A red offspring would need to have two red (R) genes. As we can see there two offspring with two red genes. Thus p ( red offspring ) =. 4 b. A white offspring would need to have two white (W) genes. As we can see there no offspring with two white genes. Thus 0 p ( white offspring ) =. 4

4 c. A red offspring would need to have one red (R) and one white (W) gene. As we can see there two offspring with one red (R) and one white (W) gene. Thus p ( pink offspring ) = If a single card is drawn from a deck of 5 cards, find each of the following probabilities: a. a black card b. a heart c. a queen d. a card below a 5 (count an ace as high) e. a card above a 9 (count an ace as high) f. a card below a 5 and above a 9 (count an ace as high) g. a card is below a 5 or above a 9 (count an ace as high) a. To find the probability that the card will be a black card, we need to first determine how many black cards there are and then divide that number by the total number of cards (5). If you look at a deck you will see that there are 6 cards which are black. Thus the probability 6 of a black card is =. 5 b. To find the probability that the card will be a heart, we need to determine how many hearts are in the deck and then divide that number by 5. If you look at a deck, you will see that there are 3 3 hearts. Thus the probability of a heart is =. 5 4 c. To find the probability that the card will be a queen, we need to determine how many queens are in the deck and then divide that number by 5. If you look at a deck, you will see that there are 4 4 queens. Thus the probability of a queen is =. 5 3 d. To find the probability that the card will be below a five, we need to determine how many cards are below a five in the deck and then divide that number by 5. This means that we are looking for all the 4s, 3s, and s. If you look at a deck, you will see that there are 4 fours, 4

5 threes, and 4 twos. Thus the probability of a card below a 5 is 3 =. 5 3 e. To find the probability that the card will be above a nine, we need to determine how many cards are above a nine in the deck and then divide that number by 5. This means that we are looking for all the 0s, jacks, queens, kings, and aces. If you look at a deck, you will see that there are 4 tens, 4 jacks, 4 queens, 4 kings, and 4 aces. Thus the 0 5 probability of a card above a 9 is =. 5 3 f. To find the probability that the card will be below a five and above a nine, we need to determine how many cards are below a five and above a nine at the same time in the deck and then divide that number by 5. There are no cards that qualify as being both below a five and above a nine at the same time. Thus the probability of a card below a 0 5 and above a 9 is = 0. 5 g. To find the probability that the card will be below a five or above a nine, we need to determine how many cards are below a five or above a nine at the same time in the deck and then divide that number by 5. Since we see the word "or" in the statement, we can use one of our probability rules p( E F ) = p( E ) + p( F ) p( E F ). If we let E be the event of a card below a five and F be the even that a card is above a 9, then we can use what we got for parts d, e, and f to answer this question. This will give us + = = Alex is taking two courses, algebra and U.S. history. Student records indicate that the probability of passing algebra is 0.5; that of failing U.S. history is 0.45; and that of passing at least one of the two courses is Find the probability of each of the following. a. Alex will pass history. b. Alex will pass both courses. c. Alex will fail both courses. d. Alex will pass exactly one course. a. Alex passing history is the complement of Alex failing history. Thus we can use what we know about the probability of an event and its

6 complement to find the probability of Alex passing history. It will be = b. The easiest way to figure this out is using the probability formula p( E F ) = p( E ) + p( F ) p( E F ). If we let E be the event that Alex passes history and F be the event that Alex passes algebra, then we have 0.80 = p( E F ). With a little simplification we get 0.80 = 0.80 p( E F ). And we finally determine that p ( E F ) = 0. In other words, the probability that Alex will pass both courses is 0. c. Alex failing both courses is the complement of Alex passing at least one of the two courses. Thus we can use what we know about complements to find the probability of Alex failing both courses. It will be = 0.0. d. The probability that Alex will pass exactly one course is the probability that Alex will pass only algebra or Alex will pass only history. Since these two things are mutually exclusive (the probability that Alex will pass both is 0), then we just need to add the probabilities together to get = Another way to calculate this is to use a table. Across the top of this you would write in one column each for pass history, fail history, and total. Along the left you would have one row each for pass algebra, fail algebra, and total. You are told that the probability of failing history is.45. This number would go in the total row at the bottom of the fail history column. You are told that the probability of passing algebra is.5. This number would go in the total column at the end of the passing algebra row. You can now fill in the other piece of the total column at the failing algebra row. Since there are only two things that can happen when it comes to algebra, the two totals must add up to. Thus at the end of the failing algebra row in the total column would be -.5. Similarly, you can fill in the total row at the bottom of the passing history column with Now the four boxes in the table where the passing and failing history overlap with passing and failing algebra cover all of the possibilities for what can happen. Thus all those 4 probabilities added together add up to. Each column must add up to the total at the bottom of the column and each row must add up to the total at the right of each row. Once we fill in one of the 4 pieces, we will be able to fill in the rest. In order

7 to do that we use the information that the probability of passing at least one of the two courses is.80. This number is the sum of the following 3 blocks -- pass history and pass algebra, pass history and fail algebra, pass algebra and fail history. In each of those cases you pass at least one of the courses. This means that the only box not covered is the fail history and fail algebra. This means that we can figure out the probability of failing both courses by calculating Once we have that we can fill in the rest of the boxes and answer the questions. pass history fail history total pass algebra fail algebra total On the basis of his previous experience, the public librarian at Smallville knows that the number of books checked out by a person visiting the library has the following probabilities Number of Books Probability Find the expected number of books checked out by a person visiting this library. To find the expected value of the number of books checked out, we need to find a "weighted average". In other words we need to take into account the probability for each number of books to calculate the average. We do this by multiplying the number of books by the probability that that number will be checked out. We add each of these products together to find the expected value. This gives us ( ) + (0.5 ) + (0.5 ) + (0.35 3) + (0.05 4) + (0.5 5) =.65. Thus the expected number of books checked out by a person visiting this library is.65.

8 6. A group of 600 people were surveyed about violence on television. Of those women surveyed, 56 said there was too much violence, 45 said that there was not too much violence, and 9 said they don t know. Of those men surveyed, 6 said there was too much violence, 95 said that there was not too much violence, and 3 said they don t know. a. What is the probability that a person surveyed was a woman and thought there was not too much violence on television? b. What is the probability that a person thought there was too much violence on television given that the person was a woman? c. What is the probability that a person who was a man thought that there was not too much violence on television? We want to organize the data into a table. This will make the information easier to use. Too Much Violence Yes No Don t Know Total Men Women Total a. For this problem we are looking for just how many people are in the women row and also in the no columns. This number is 45. We then take this number and divide it by the total number of people surveyed 45 to get the probability of = b. The part written as "given that the person was a woman" tells us to look only in the women row and use the total number of women as 30 as out total to divide by. In the women row there were 56 who thought that there was too much violence. When we take 56 and divide it by 30 we get the probability that a person though there was too much violence given that the person was a women. This probability is 56 = c. The part written as "who was a man" tells us to look only in the men row and use the total number of men as 80 as our total to divide by. In the men row there were 95 who thought that there was not too much violence. When we take 95 and divide it by 80 we get the

9 probability that a person thought there was too much violence given that the person was a man. This probability is 95 =

### EXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS

EXAM Exam #3 Math 1430, Spring 2002 April 21, 2001 ANSWERS i 60 pts. Problem 1. A city has two newspapers, the Gazette and the Journal. In a survey of 1, 200 residents, 500 read the Journal, 700 read the

### Counting principle, permutations, combinations, probabilities

Counting Methods Counting principle, permutations, combinations, probabilities Part 1: The Fundamental Counting Principle The Fundamental Counting Principle is the idea that if we have a ways of doing

### Construct and Interpret Binomial Distributions

CH 6.2 Distribution.notebook A random variable is a variable whose values are determined by the outcome of the experiment. 1 CH 6.2 Distribution.notebook A probability distribution is a function which

### Lecture 14. Chapter 7: Probability. Rule 1: Rule 2: Rule 3: Nancy Pfenning Stats 1000

Lecture 4 Nancy Pfenning Stats 000 Chapter 7: Probability Last time we established some basic definitions and rules of probability: Rule : P (A C ) = P (A). Rule 2: In general, the probability of one event

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Provide an appropriate response. 1) A coin is tossed. Find the probability that the result

### Probability: The Study of Randomness Randomness and Probability Models. IPS Chapters 4 Sections 4.1 4.2

Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4 Sections 4.1 4.2 Chapter 4 Overview Key Concepts Random Experiment/Process Sample Space Events Probability Models Probability

### PROBABILITY. Chapter Overview

Chapter 6 PROBABILITY 6. Overview Probability is defined as a quantitative measure of uncertainty a numerical value that conveys the strength of our belief in the occurrence of an event. The probability

### Section 6.2 ~ Basics of Probability. Introduction to Probability and Statistics SPRING 2016

Section 6.2 ~ Basics of Probability Introduction to Probability and Statistics SPRING 2016 Objective After this section you will know how to find probabilities using theoretical and relative frequency

### If we know that LeBron s next field goal attempt will be made in a game after 3 days or more rest, it would be natural to use the statistic

Section 7.4: Conditional Probability and Tree Diagrams Sometimes our computation of the probability of an event is changed by the knowledge that a related event has occurred (or is guaranteed to occur)

### Probability. Vocabulary

MAT 142 College Mathematics Probability Module #PM Terri L. Miller & Elizabeth E. K. Jones revised January 5, 2011 Vocabulary In order to discuss probability we will need a fair bit of vocabulary. Probability

### Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution

Recall: Ch5: Discrete Probability Distributions Section 5-1: Probability Distribution A variable is a characteristic or attribute that can assume different values. o Various letters of the alphabet (e.g.

### I. WHAT IS PROBABILITY?

C HAPTER 3 PROBABILITY Random Experiments I. WHAT IS PROBABILITY? The weatherman on 0 o clock news program states that there is a 20% chance that it will snow tomorrow, a 65% chance that it will rain and

### Lesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314

Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space

### Tree Diagrams. on time. The man. by subway. From above tree diagram, we can get

1 Tree Diagrams Example: A man takes either a bus or the subway to work with probabilities 0.3 and 0.7, respectively. When he takes the bus, he is late 30% of the days. When he takes the subway, he is

### Review of Probability

Review of Probability Table of Contents Part I: Basic Equations and Notions Sample space Event Mutually exclusive Probability Conditional probability Independence Addition rule Multiplicative rule Using

### Lesson #1.7-Incomplete Dominance Codominance Dihybrid Crosses

Lesson #1.7-Incomplete Dominance Codominance Dihybrid Crosses Exceptions to Mendel s principles So far, offspring have either the phenotype of one parent or the other. Sometimes, there is no dominant or

### Probability. Sample space: all the possible outcomes of a probability experiment, i.e., the population of outcomes

Probability Basic Concepts: Probability experiment: process that leads to welldefined results, called outcomes Outcome: result of a single trial of a probability experiment (a datum) Sample space: all

### Name Date Period. Review on Incomplete Dominance/ Codominance and Multiple Alleles

Pollen Name DatePeriod Review on Incomplete Dominance/ Codominance and Multiple Alleles 1. In snapdragon flowers, the red (C R ) and white (C W ) flower color alleles exhibit incomplete dominance. Flowers

### The rule for computing conditional property can be interpreted different. In Question 2, P B

Question 4: What is the product rule for probability? The rule for computing conditional property can be interpreted different. In Question 2, P A and B we defined the conditional probability PA B. If

### An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event

An event is any set of outcomes of a random experiment; that is, any subset of the sample space of the experiment. The probability of a given event is the sum of the probabilities of the outcomes in the

### Opening Activity: Latin Root Word: Review of Old Information:

Section: 3.4 Opening Activity: Latin Root Word: Review of Old Information: Name: 1. In seals, the allele for long whiskers (L) is dominant and the allele for short whiskers (l) is recessive. What are the

### Laws of probability. Information sheet. Mutually exclusive events

Laws of probability In this activity you will use the laws of probability to solve problems involving mutually exclusive and independent events. You will also use probability tree diagrams to help you

### Ch.12 Reading and Concept Review Packet /20

Name: Period: Date: Ch.12 Reading and Concept Review Packet /20 Term Chapter 12 Reading and Concept Review: page 308-333. Directions: Link the various terms into coherent sentence or two that connects

### BRIEF SOLUTIONS. Basic Probability WEEK THREE. This worksheet relates to chapter four of the text book (Statistics for Managers 4 th Edition).

BRIEF SOLUTIONS Basic Probability WEEK THREE This worksheet relates to chapter four of the text book (Statistics for Managers 4 th Edition). This topic is the one many students find the most difficult.

### Dr. Young. Genetics Problems Set #1 Answer Key

BIOL276 Dr. Young Name Due Genetics Problems Set #1 Answer Key For problems in genetics, if no particular order is specified, you can assume that a specific order is not required. 1. What is the probability

### Key Concept. Properties

MAT 155 Statistical Analysis Dr. Claude Moore Cape Fear Community College Chapter 6 Normal Probability Distributions 6 1 Review and Preview 6 2 The Standard Normal Distribution 6 3 Applications of Normal

### Review for Test 2. Chapters 4, 5 and 6

Review for Test 2 Chapters 4, 5 and 6 1. You roll a fair six-sided die. Find the probability of each event: a. Event A: rolling a 3 1/6 b. Event B: rolling a 7 0 c. Event C: rolling a number less than

### Exam. Name. How many distinguishable permutations of letters are possible in the word? 1) CRITICS

Exam Name How many distinguishable permutations of letters are possible in the word? 1) CRITICS 2) GIGGLE An order of award presentations has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm,

### Probability and Counting Rules

blu3496x_ch04.qxd 7/6/06 0:49 AM Page 77 B&W CONFIRMINGS C H A P T E R 4 Probability and Counting Rules Objectives Outline After completing this chapter, you should be able to 4 Determine sample spaces

### Bell Work: Friday, December 14. If red is dominant to white in flowers, how do we get pink ones?

Bell Work: Friday, December 14 If red is dominant to white in flowers, how do we get pink ones? 1 Review We have discussed human traits that have two completely different phenotypes (physical appearances)

### Grade 7/8 Math Circles Fall 2012 Probability

1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Probability Probability is one of the most prominent uses of mathematics

### Ch. 13.3: More about Probability

Ch. 13.3: More about Probability Complementary Probabilities Given any event, E, of some sample space, U, of a random experiment, we can always talk about the complement, E, of that event: this is the

### Definition/Example Signature

Engage: Who Remembers? Instructions: Discuss the following terms with other students. Try to find someone who can explain the term to you or give you an example of the term. Record the definition or example

Chance deals with the concepts of randomness and the use of probability as a measure of how likely it is that particular events will occur. A National Statement on Mathematics for Australian Schools, 1991

### Poker. 10,Jack,Queen,King,Ace. 10, Jack, Queen, King, Ace of the same suit Five consecutive ranks of the same suit that is not a 5,6,7,8,9

Poker Poker is an ideal setting to study probabilities. Computing the probabilities of different will require a variety of approaches. We will not concern ourselves with betting strategies, however. Our

### Example: If we roll a dice and flip a coin, how many outcomes are possible?

12.5 Tree Diagrams Sample space- Sample point- Counting principle- Example: If we roll a dice and flip a coin, how many outcomes are possible? TREE DIAGRAM EXAMPLE: Use a tree diagram to show all the possible

### Texas Hold em. From highest to lowest, the possible five card hands in poker are ranked as follows:

Texas Hold em Poker is one of the most popular card games, especially among betting games. While poker is played in a multitude of variations, Texas Hold em is the version played most often at casinos

Probability Worksheet 2 NAME: Remember to leave your answers as unreduced fractions. We will work with the example of picking poker cards out of a deck. A poker deck contains four suits: diamonds, hearts,

### GENETIC CROSSES. Monohybrid Crosses

GENETIC CROSSES Monohybrid Crosses Objectives Explain the difference between genotype and phenotype Explain the difference between homozygous and heterozygous Explain how probability is used to predict

### Genetics Exam Review Questions

Name: Date: Genetics Exam Review Questions Multiple Choice: Select the best answer to complete each statement. 1. Mendel crossed pea plants with greens seeds (yy) with plants with yellow seeds (YY). The

### Reasoning Strategies for Addition Facts

Reasoning Strategies for Addition Facts More Than One and Two More Than There are 36 addition facts on the chart that have at least one addend (number being added to another) of 1 or 2. Being able to count

### Fundamentals of Probability

Fundamentals of Probability Introduction Probability is the likelihood that an event will occur under a set of given conditions. The probability of an event occurring has a value between 0 and 1. An impossible

### Find the indicated probability. 1) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.

Math 0 Practice Test 3 Fall 2009 Covers 7.5, 8.-8.3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated probability. ) If a single

### Mendelian Genetics. Lab Exercise 13. Contents. Objectives. Introduction

Lab Exercise Mendelian Genetics Contents Objectives 1 Introduction 1 Activity.1 Forming Gametes 2 Activity.2 Monohybrid Cross 3 Activity.3 Dihybrid Cross 4 Activity.4 Gene Linkage 5 Resutls Section 8 Objectives

### 7.1 Sample space, events, probability

7.1 Sample space, events, probability In this chapter, we will study the topic of probability which is used in many different areas including insurance, science, marketing, government and many other areas.

### Mendelian Genetics and Inheritance Problems

Biology 211 Mendelian Genetics and Inheritance Problems Mendel discovered and described many of the basic rules of genetics after studying the pattern of how inheritable traits were passed from generation

### Math 117 Chapter 7 Sets and Probability

Math 117 Chapter 7 and Probability Flathead Valley Community College Page 1 of 15 1. A set is a well-defined collection of specific objects. Each item in the set is called an element or a member. Curly

### Probability: The Study of Randomness Randomness and Probability Models

Probability: The Study of Randomness Randomness and Probability Models IPS Chapters 4.1 and 4.2 2009 W.H. Freeman and Company Objectives (IPS Chapters 4.1 and 4.2) Randomness and Probability models Probability

### Main Effects and Interactions

Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly

### Question of the Day. Key Concepts. Vocabulary. Mathematical Ideas. QuestionofDay

QuestionofDay Question of the Day What is the probability that in a family with two children, both are boys? What is the probability that in a family with two children, both are boys, if we already know

### Chapter 4 Probability

The Big Picture of Statistics Chapter 4 Probability Section 4-2: Fundamentals Section 4-3: Addition Rule Sections 4-4, 4-5: Multiplication Rule Section 4-7: Counting (next time) 2 What is probability?

### Statistics 100A Homework 2 Solutions

Statistics Homework Solutions Ryan Rosario Chapter 9. retail establishment accepts either the merican Express or the VIS credit card. total of percent of its customers carry an merican Express card, 6

### Homework 2 Solutions

CSE 21 - Winter 2012 Homework #2 Homework 2 Solutions 2.1 In this homework, we will consider ordinary decks of playing cards which have 52 cards, with 13 of each of the four suits (Hearts, Spades, Diamonds

### 3. If a heterozygous fire-breathing dragon is crossed with one that does not breathe fire, how many offspring will be fire breathers?

Mrs. Davisson Name Chapter 11: Genetics Per. Row Part I. Monohybrid Crosses - Complete Dominance For each of the following genetics problems, follow these steps in reaching a complete answer: Show all

### Elementary Statistics. Probability Rules with Venn & Tree Diagram

Probability Rules with Venn & Tree Diagram What are some basic Probability Rules? There are three basic Probability Rules: Complement Rule Addition Rule Multiplication Rule What is the Complement Rule?

### Probability. A random sample is selected in such a way that every different sample of size n has an equal chance of selection.

1 3.1 Sample Spaces and Tree Diagrams Probability This section introduces terminology and some techniques which will eventually lead us to the basic concept of the probability of an event. The Rare Event

### Chapter 15. Definitions: experiment: is the act of making an observation or taking a measurement.

MATH 11008: Probability Chapter 15 Definitions: experiment: is the act of making an observation or taking a measurement. outcome: one of the possible things that can occur as a result of an experiment.

### 11.1 The Work of Gregor Mendel

11.1 The Work of Gregor Mendel Lesson Objectives Describe Mendel s studies and conclusions about inheritance. Describe what happens during segregation. Lesson Summary The Experiments of Gregor Mendel The

### Probability OPRE 6301

Probability OPRE 6301 Random Experiment... Recall that our eventual goal in this course is to go from the random sample to the population. The theory that allows for this transition is the theory of probability.

### 2urbo Blackjack 21.99. 2 9 Hold their face value

2urbo Blackjack Type of Game The game of 2urbo Blackjack utilizes a player-dealer position and is a California game. The player-dealer shall collect all losing wagers, pay all winning wagers, and may not

### Puzzle Solutions. 2. Count the Bricks.

Puzzle Solutions Puzzle Solutions 1. Train. A train one mile long travels at the rate of one mile a minute through a tunnel which is one mile long. How long will it take the train to pass completely through

### If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?

Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question

### The study of probability has increased in popularity over the years because of its wide range of practical applications.

6.7. Probability. The study of probability has increased in popularity over the years because of its wide range of practical applications. In probability, each repetition of an experiment is called a trial,

### frequency of E sample size

Chapter 4 Probability (Page 1 of 24) 4.1 What is Probability? Probability is a numerical measure between 0 and 1 that describes the likelihood that an event will occur. Probabilities closer to 1 indicate

### PROBABILITY 14.3. section. The Probability of an Event

4.3 Probability (4-3) 727 4.3 PROBABILITY In this section In the two preceding sections we were concerned with counting the number of different outcomes to an experiment. We now use those counting techniques

### TEST NAME: Genetics unit test TEST ID: GRADE:07 SUBJECT:Life and Physical Sciences TEST CATEGORY: School Assessment

TEST NAME: Genetics unit test TEST ID: 437885 GRADE:07 SUBJECT:Life and Physical Sciences TEST CATEGORY: School Assessment Genetics unit test Page 1 of 12 Student: Class: Date: 1. There are four blood

### Not all traits are simply inherited by dominant and recessive alleles (Mendelian Genetics). In some traits, neither allele is dominant or many

Not all traits are simply inherited by dominant and recessive alleles (Mendelian Genetics). In some traits, neither allele is dominant or many alleles control the trait. Below are different ways in which

### 4.3. Addition and Multiplication Laws of Probability. Introduction. Prerequisites. Learning Outcomes. Learning Style

Addition and Multiplication Laws of Probability 4.3 Introduction When we require the probability of two events occurring simultaneously or the probability of one or the other or both of two events occurring

### Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded

Combinations If 5 sprinters compete in a race, how many different ways can the medals for first, second and third place, be awarded If 5 sprinters compete in a race and the fastest 3 qualify for the relay

### Simple Random Sampling

Source: Frerichs, R.R. Rapid Surveys (unpublished), 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling, but few use this method for

### Contemporary Mathematics- MAT 130. Probability. a) What is the probability of obtaining a number less than 4?

Contemporary Mathematics- MAT 30 Solve the following problems:. A fair die is tossed. What is the probability of obtaining a number less than 4? What is the probability of obtaining a number less than

### MANDELIAN GENETICS. Crosses that deviate from Mandelian inherintance

MANDELIAN GENETICS Crosses that deviate from Mandelian inherintance Explain codominant alleles. TO THE STUDENTS Calculate the genotypic and phenotypic ratio (1:2:1). Explain incomplete dominant alleles.

### The Function Game: Can You Guess the Secret?

The Function Game: Can You Guess the Secret? Copy the input and output numbers for each secret given by your teacher. Write your guess for what is happening to the input number to create the output number

### Name: Period: Date: PAP Meiosis, Genetics & Heredity Test Review KEY

Name: Period: Date: PAP Meiosis, Genetics & Heredity Test Review KEY 1. How are an organism s complex traits determined? DNA contains codes for proteins which are necessary for growth an functioning in

### Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR.

Exam 3 Review/WIR 9 These problems will be started in class on April 7 and continued on April 8 at the WIR. 1. Urn A contains 6 white marbles and 4 red marbles. Urn B contains 3 red marbles and two white

### Mendelian Genetics. I. Background

Mendelian Genetics Objectives 1. To understand the Principles of Segregation and Independent Assortment. 2. To understand how Mendel s principles can explain transmission of characters from one generation

### Probability. Section 9. Probability. Probability of A = Number of outcomes for which A happens Total number of outcomes (sample space)

Probability Section 9 Probability Probability of A = Number of outcomes for which A happens Total number of outcomes (sample space) In this section we summarise the key issues in the basic probability

### Pure Math 30: Explained! 334

www.puremath30.com 334 Lesson 2, Part One: Basic Combinations Basic combinations: In the previous lesson, when using the fundamental counting principal or permutations, the order of items to be arranged

### LECTURE 3. Probability Computations

LECTURE 3 Probability Computations Pg. 67, #42 is one of the hardest problems in the course. The answer is a simple fraction there should be a simple way to do it. I don t know a simple way I used the

### Elementary Algebra. Section 0.4 Factors

Section 0.4 Contents: Definitions: Multiplication Primes and Composites Rules of Composite Prime Factorization Answers Focus Exercises THE MULTIPLICATION TABLE x 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5

### Chapter 14 From Randomness to Probability

Chapter 14 From Randomness to Probability 199 Chapter 14 From Randomness to Probability 1. Sample spaces. a) S = { HH, HT, TH, TT} All of the outcomes are equally likely to occur. b) S = { 0, 1, 2, 3}

### Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets

Learn How to Use The Roulette Layout To Calculate Winning Payoffs For All Straight-up Winning Bets Understand that every square on every street on every roulette layout has a value depending on the bet

### Basic Probability Theory II

RECAP Basic Probability heory II Dr. om Ilvento FREC 408 We said the approach to establishing probabilities for events is to Define the experiment List the sample points Assign probabilities to the sample

### Probability Theory, Part 4: Estimating Probabilities from Finite Universes

8 Resampling: The New Statistics CHAPTER 8 Probability Theory, Part 4: Estimating Probabilities from Finite Universes Introduction Some Building Block Programs Problems in Finite Universes Summary Introduction

### Genetics Problem Set

AP Biology Name: Genetics Problem Set Independent Assortment Problems 1. One gene has alleles A and a. Another has alleles B and b. For each genotype listed, what type(s) of gametes will be produced? (Assume

### Probabilities of Poker Hands with Variations

Probabilities of Poker Hands with Variations Jeff Duda Acknowledgements: Brian Alspach and Yiu Poon for providing a means to check my numbers Poker is one of the many games involving the use of a 52-card

### Chapter 4 - Systems of Equations and Inequalities

Math 233 - Spring 2009 Chapter 4 - Systems of Equations and Inequalities 4.1 Solving Systems of equations in Two Variables Definition 1. A system of linear equations is two or more linear equations to

### Section Tree Diagrams. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 12.5 Tree Diagrams What You Will Learn Counting Principle Tree Diagrams 12.5-2 Counting Principle If a first experiment can be performed in M distinct ways and a second experiment can be performed

### Math 2001 Homework #10 Solutions

Math 00 Homework #0 Solutions. Section.: ab. For each map below, determine the number of southerly paths from point to point. Solution: We just have to use the same process as we did in building Pascal

### 6.3 Conditional Probability and Independence

222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted

### 6.1: Beyond Mendel s Observations of Inheritance pg. 242

6.1: Beyond Mendel s Observations of Inheritance pg. 242 Incomplete Dominance Incomplete dominance: is condition in which neither allele for a gene completely conceals the presence of the other; it results

### What is Genetics? Genetics is the scientific study of heredity

What is Genetics? Genetics is the scientific study of heredity What is a Trait? A trait is a specific characteristic that varies from one individual to another. Examples: Brown hair, blue eyes, tall, curly

### Homework 3 Solution, due July 16

Homework 3 Solution, due July 16 Problems from old actuarial exams are marked by a star. Problem 1*. Upon arrival at a hospital emergency room, patients are categorized according to their condition as

### VISUAL ALGEBRA FOR COLLEGE STUDENTS. Laurie J. Burton Western Oregon University

VISUAL ALGEBRA FOR COLLEGE STUDENTS Laurie J. Burton Western Oregon University VISUAL ALGEBRA FOR COLLEGE STUDENTS TABLE OF CONTENTS Welcome and Introduction 1 Chapter 1: INTEGERS AND INTEGER OPERATIONS

### MEP Pupil Text 12. A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued.

MEP Pupil Text Number Patterns. Simple Number Patterns A list of numbers which form a pattern is called a sequence. In this section, straightforward sequences are continued. Worked Example Write down the

### Chapter 11 Genetics. STATE FRAMEWORKS 3. Genetics

STATE FRAMEWORKS 3. Genetics Chapter 11 Genetics Central Concepts: Genes allow for the storage and transmission of genetic information. They are a set of instructions encoded in the nucleotide sequence