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

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1 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 results when 1 coin is flipped 3 times. a) List the elements that make up the sample space. b) How many outcomes are possible? c) ( ) d) ( )

2 Example: 3 Marbles in a bag 1 red, 1 silver, 1 black A) WITH REPLACEMENT- PICK 2 1) How many outcomes? 2) Sample Space: 3) ( ) 4) ( ) 5) ( ) B) Without replacement 1) How many outcomes? 2) Sample Space: 3) ( ) 4) ( ) 5) ( )

3 12.5 Practice Problems 1) There are 3 cards in a hat; one is a king, one is a queen, and one is an ace. Two cards are to be selected at random with replacement. Using a tree diagram, obtain the sample space for the experiment. a) List the elements that make up the sample space. b) Find the probability that you choose the same card twice. c) Find the probability that a king and a queen are selected. 2) There are 3 cards in a hat; one is a King, one is a Queen, and one is an Ace. Two cards are to be selected at random without replacement. Using a tree diagram, obtain the sample space for the experiment. a) List the elements that make up the sample space. b) Find the probability that you choose the same card twice. c) Find the probability that a king and a queen are selected.

4 3) A couple plans to have four children. Using a tree diagram, obtain the sample space. a) List the elements that make up the sample space. b) Find the probability that the family has three boys first and then one girl. c) Find the probability that the family has at least one boy. d) Find the probability that the family has no boys. 4) A sports shop sold tennis rackets in 2 different weights, 3 types of string, and 4 grip sizes. How many different rackets could they sell? 5) A local department store sold carpets in 4 sizes. Each carpet came in 3 qualities. One size of carpet came in 7 colors. The other sizes came in 4 colors. How many choices of carpet were there?

5 12.6 Compound Probability : OR and AND Problems OR probability problem P(A or B)= P(A U B) Example 1: Roll a die. Find P ( Odd or Prime). Example 2: Sample space is # s Find P(number is less than 4 or greater than 7) Mutually exclusive- Example 3: Find P(A or B) if 1 card is selected from a deck. a) A= an ace B=a king b) A= an ace B= a heart c) A = red card B= black card d) A=a picture card B = red card

6 AND Probability Problems P(A and B)= P(A B) Example 4: A bag contains 3 chips: R, B, G. Select 2 chips with Replacement. 1) P(Red and Blue in that order) Tree Diagram: Independent Events- Dependent Events-

7 12.6 Practice Problems 1) If P(A) = 0.6, P(B) = 0.3, and P(A and B) = 0.1, find P(A or B). 2) If P(A) = 0.5, P(B) = 0.4, and P(A or B) = 0.7, find P(A and B). 3) If P(B) = 0.3, P(A or B) = 0.4, and P(A and B) = 0.5, find P(A). 4) If P(A) = 0.2, P(A or B) = 0.3, and P(A and B) = 0.5, find P(B). 5) A 6-sided die is rolled. What is the probability of rolling a 3 or a 5? 6) A lottery game has balls numbered 0 through 13. What is the probability of selecting an even numbered ball or a 7? 7) One card is selected from a deck of cards. Find the probability of selecting a black card or a king. 8) One card is selected from a deck of cards. Find the probability of selecting a black card or a card less than 8. (Note: The ace is considered a low card.) 9) One card is selected from a deck of cards. Find the probability of selecting a diamond or a card less than 7. (Note: The ace is considered a low card.)

8 10) A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a spade? 11) A family has five children. The probability of having a girl is 1/2. What is the probability of having 2 girls followed by 3 boys? 12) If you are dealt two cards successively (with replacement of the first) from a standard 52- card deck, find the probability of getting a face card on the first card and an ace on the second. 13) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 5 possible answers. 14) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. 15) You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a king and the second card is a queen. When to use which formula: OR problems will almost always contain the word or in the statement of the problem. For example, find the probability of selecting a heart or a 6. Or problems in this book generally involve only one selection. For example, one card is selected, or one die is rolled. AND problems will often not use the word AND in the statement of the problem. For example, find the probability that both cards selected are red, or find the probability that none of those selected is a banana are both AND type problems. And problems in this section will generally involve more than 1 selection. For example, the problem may read two cards are selected, or 3 coins are flipped.

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