Probability Sample Test

Transcription

1 Name: Class: Date: ID: A Probability Sample Test Multiple Choice Identify the choice that best completes the statement or answers the question.. A coin is tossed three times. What is the probability of tossing exactly two heads? A standard die is rolle What is the probability of rolling a? 2. A computerized random number generator generates a number between and 00 for a lottery. What is the probability that it is divisible by? Which of the following statements is false? Theoretical probability is also called classical probability or a priori probability. Experimental probability is another term for relative-frequency probability. A sample space is the set of all possible outcomes of a probability experiment. Empirical probability is another term for subjective probability. 5. Two identical spinners each have five equal sectors that are numbered to 5. What is the probability of a total less than 9 when you spin both these spinners? If the odds in favour of snow tomorrow are :7, what is the probability of snow tomorrow? Two dice are rolled and the upper faces are recorde What are the odds against the sum of the two dice being? : : 7: :7. Twelve books are placed on a shelf in random order. What is the probability that their titles are in alphabetical order? 2 2! C 2 9. Five different letters are randomly selected from the alphabet. What is the probability that they are A, B, C, D and E? 5 5! 26 C 5 26 P 5 0. Eight children line up for a photograph. What is the probability that they will be in ascending order of their ages?!! C 26 C P 2 26 C 5

2 Name: ID: A. Five cards are laid face up on a table. What is the probability that the first card is a king and the last card is an ace? P P P P P 2 52 P 5 2. Six people were asked to randomly select a food from a list of 20 foods. What is the probability that at least two people select the same food? P(20,6) C 2 P(20,6) P(20,6) 52 P 2 20 P(20,6). Which of the following pairs of events are dependent? rolling a die; dealing a card from a standard deck rolling a 6 on one die; rolling a 6 on a second die rolling doubles with two dice; rolling an even sum with two dice dealing a king from a standard deck; spinning a on a spinner. Which of the following pairs of events are independent? being dealt the king of hearts from a standard deck; being dealt the king of clubs in the same hand selecting the winning lottery number; selecting the second place lottery number on a different ticket the first coin shows heads; three out of four coins show heads the first person selected is male; the fifth person selected is female 5. Of all the students at Eastern Collegiate, 55% were born in Canad Of those born in Canada, 5% speak English at home. Of those not born in Canada, 2% speak English at home. A student was selected at random. What is the probability that this student was born in Canada or speaks English at home? A newspaper sports reporter has a 5% accuracy for predicting the winners in NHL hockey games. A radio sports reporter has a 65% accuracy for predicting the winners. For a particular game, what is the probability that at least one of these reporters will make a correct prediction? When two events are mutually exclusive, it means that there is an intersection between the two events the probability of one event depends on the probability of the other the two events cannot occur at the same time the two events are equally likely. If P(A) = 0. and P(B) = 0.2, and A and B are mutually exclusive events, which one of the following statements is true? P(A and B) = 0.6 P(A and B) = 0 P(A or B) = 0.0 P(A or B) = 0.2 2

3 Name: ID: A Consider the Venn diagram below, with the number of items in each set indicate One item is selected from the universal set. 9. Which is a true statement? Events A and B are mutually exclusive. Events A and B are non-mutually exclusive. Events A and B are dependent. Event B is the complement of event A. 20. P(A or B) = Short Answer 2. Explain the meaning of the terms in the probability formula, P(A) = n(a) n(s). 22. A coin is tossed three times. What is the probability of tossing at least one head? 2. A standard die is rolle What is the probability of rolling a prime number? 2. Two standard dice are rolle What is the probability that a sum less than 7 is not rolled? 25. What are the odds in favour of July st being a Tuesday? 26. If the odds are 9 : against the next car you see being red, what percent of cars in your area are red? 27. A club with eight members from grade and five members from grade 2 is to elect a president, vice-president, and secretary. What is the probability that grade 2 students will be elected for all three positions, assuming that all club members have an equal chance of being elected? Give your answer as a percent, rounded to one decimal place. 2. A four-member curling team is randomly chosen from six grade- students and nine grade-2 students. What is the probability that the team has at least one grade- student? 29. Four students are selected at random from a group of three girls and five boys. What is the probability that two girls and two boys will be selected?

4 Name: ID: A 0. Lesley-Anne estimates that she has a 75% chance of passing physics and an 0% chance of passing English. Assume that {passing English} and {passing Physics} are independent events. a) What is the probability that Lesley-Anne will pass only one of these two subjects? b) What are the odds in favour of Lesley-Anne failing both subjects?. If a satellite launch has a 97% chance of success, what is the probability of three consecutive successful launches? 2. The probability that Jacqueline will be elected to the students council is 0.6, and the probability that she will be selected to represent her school in a public-speaking contest is The probability of Jacqueline achieving both of these goals is 0.5. a) Are these two goals mutually exclusive? Explain your answer. b) What is the probability that Jacqueline is either elected to the students council or picked for the public-speaking contest? c) What is the probability that she fails to be selected for either the students council or the public-speaking contest?. The probability that Sarjay will play golf today is 60%, the probability that he will play golf tomorrow is 75%, and the probability that he will play golf on both days is 50%. What is the probability that he does not play golf on either day? Problem. Suppose you randomly draw two marbles, without replacement, from a bag containing six green, four red, and three black marbles. a) Draw a tree diagram to illustrate all possible outcomes of this draw. b) Determine the probability that both marbles are re c) Determine the probability that you pick at least one green marble. 5. A survey at a school asked students if they were ill with a cold or the flu during the last month. The results were as follows. None of the students had both a cold and the flu. Cold Flu Healthy Females 2 7 Males 25 9 Use these results to estimate the probability that a) a randomly selected student had a cold in the last month b) a randomly selected female student was healthy last month c) a randomly selected student is male given that they have the flu d) a randomly selected student has a cold or flue given that the student is male 6. To get out of jail free in the board game MONOPOLY, you have to roll doubles with a pair of standard dice. Determine the odds in favour of getting out of jail on your first or second roll.

5 Probability Sample Test Answer Section MULTIPLE CHOICE. ANS: D PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6. LOC: A. TOP: Counting and Probability 2. ANS: D PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6. LOC: A. TOP: Counting and Probability. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6. LOC: A. TOP: Counting and Probability. ANS: D PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6. LOC: A. TOP: Counting and Probability 5. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6. LOC: A. TOP: Counting and Probability 6. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.2 LOC: A.5 TOP: Counting and Probability KEY: odds and probability 7. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.2 LOC: A.5 TOP: Counting and Probability KEY: odds. ANS: B PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 9. ANS: B PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 0. ANS: A PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability. ANS: D PTS: DIF: REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 2. ANS: A PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability. ANS: C PTS: DIF: 2 REF: Knowledge & Understanding OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events. ANS: B PTS: DIF: 2 REF: Knowledge & Understanding OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events

6 5. ANS: B PTS: DIF: 2 REF: Application OBJ: Section 6.5 LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events 6. ANS: C PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events 7. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events 9. ANS: A PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events 20. ANS: C PTS: DIF: REF: Knowledge & Understanding OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events SHORT ANSWER 2. ANS: P represents probability. A represents the event A. The letter n stands for number and n(a) represents the number of outcomes in which event A occurs. S represents the sample space, and n(s) is the number of outcomes in the sample space (the total number of possible outcomes). PTS: DIF: REF: Communication OBJ: Section 6. LOC: A. TOP: Counting and Probability concepts 22. ANS: 7 PTS: DIF: 2 REF: Knowledge & Understanding OBJ: Section 6. LOC: A. A.5 TOP: Counting and Probability 2. ANS: 2 PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A. TOP: Counting and Probability 2

7 2. ANS: 7 2 PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A.5 TOP: Counting and Probability KEY: complement 25. ANS: : 6 PTS: DIF: REF: Application OBJ: Section 6.2 LOC: A.5 TOP: Counting and Probability KEY: odds 26. ANS: 0% PTS: DIF: 2 REF: Application OBJ: Section 6.2 LOC: A.5 TOP: Counting and Probability KEY: odds 27. ANS: 5 P P = % PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 2. ANS: 9C 5 C = = PTS: DIF: REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 29. ANS: C 2 5 C 2 C = 0 70 = 7 PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability

8 0. ANS: a) 0.75 ( 0.) + ( 0.75) 0. = 0.5 b) P(failing both) = = 0.05 Odds in favour = 5 : 95 = : 9 PTS: DIF: REF: Application OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events. ANS: ( 0.97) = PTS: DIF: 2 REF: Application OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events 2. ANS: a) The two goals cannot be mutually exclusive since the probability of achieving both is 0.5. b) = 0.5 c) 0.5 = 0.5 (Use a Venn diagram) PTS: DIF: REF: Application Communication OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events. ANS: 00% (60% + 75% 50%) = 5% PTS: DIF: 2 REF: Application OBJ: Section 6.5 LOC: A.5 TOP: Counting and Probability KEY: mutually exclusive events

9 PROBLEM. ANS: a) b) P(both red) = C 2 9 C 0 C 2 = 6 7 = c) P(at least one green) = P(one green) + P(two greens) Ê Ë Á = 6C C ˆ + Ê C 7 Ë Á C ˆ = 7 = 9 26 C 2 PTS: DIF: REF: Application OBJ: Section 6. LOC: A2.5 TOP: Counting and Probability 5

10 5. ANS: a) P(cold) = =Ö 0. or about.% P(A and B) b) Using the conditional probability formula, P(A B) = : P(B) P(healthy female) = = 7 97 =Ö 0.5 or about.5% c) Restricting the sample space to only those who had the flu, P(male flu) = 9 d) Restricting the sample space to only males, P(cold or flu male) = 2 =Ö or about 5.7% 7 =Ö 0.55 or about 5.% PTS: DIF: REF: Application OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events 6. ANS: The probability of rolling doubles on the first roll is 6 6 =. The probability of not rolling doubles on the 6 first roll is 5 6. Therefore, the probability of rolling doubles on the second roll is = 5 6. The probability of rolling doubles on the first roll or the second roll is = 6. Thus, the odds in favour of getting out of jail on either the first or second try are : 25. PTS: DIF: REF: Thinking OBJ: Section 6. LOC: A.6 TOP: Counting and Probability KEY: dependent and independent events 6