Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Bellringer

Transcription

1 Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Bellringer Use the following information below to answer the two following questions: Students are playing a game that requires spinning the two spinners shown below. Green Yellow 1. Which of the following represents the sample space for this game? a. {RR,RB,RY,RG,BB,BY,BG,BR} b. {RB, RBYG} c. {RB,RY,RG,BY,BG,BR} d. {2,4} 2. Which of the following represents the probability of spinning two reds? a. 0.5 b c d. 0.75

2 Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Notes Example 1: Students are playing a game that requires spinning the two spinners shown below. List the sample space of possible outcomes below: Green Yellow Instead of just listing the outcomes we can also create a Tree Diagram that outlines how each action connects to the next, eventually creating a single event that we can find the probability of. a. What is the probability of spinning two reds? b. What is the probability of spinning a different color on both spins? c. What is the probability of not spinning green.

3 Example 2: Draw a tree diagram outlining the outcomes of flipping a coin twice? What is the probability of getting a heads on the first flip and a tails on the second? Example 2: Imagine that a family decides to play a game each night. They all agree to use a tetrahedral die (located at right) each night to randomly determine if they will play a board game (B) or a card game (C). The tree diagram mapping the possible overall outcomes over two consecutive nights will be developed below. To make a tree diagram, first present all possibilities for the first stage. (In this case, Monday.) Monday Tuesday Outcome B C a. If BB represents two straight nights of board games, what does CB represent? b. List the outcomes where exactly one board game is played over two days. How many outcomes were there?

4 Homework: 1) Which tree diagram shows all of the possible outcomes for tossing a coin and rolling a fair number pyramid that has four sides labeled 1 through 4? 2) An owner of a small store knows that in the last week, 44 customers paid with cash, 13 paid with a debit card, and 143 paid with a credit card. Which below is closest to the probability of a person paying with a debit card? a b c d. 0.78

5 3) Imagine that a family of three (Alice, Bill, and Chester) plays bingo at home every night. Each night, the chance that any one of the three players will win is 1 3. a. Using A for Alice wins, B for Bill wins, and C for Chester wins, develop a tree diagram that shows the nine possible outcomes for two consecutive nights of play. b. Is the probability that Bill wins both nights" the same as the probability that Alice wins the first night and Chester wins the second night? Explain. 4) In a laboratory experiment, two mice will be placed in a simple maze with one decision point where a mouse can turn either left (L) or right (R). When the first mouse arrives at the decision point, the direction it chooses is recorded. Then, the process is repeated for the second mouse. a. Draw a tree diagram where the first stage represents the decision made by the first mouse, and the second stage represents the decision made by the second mouse. Determine all four possible decision outcomes for the two mice.

6 Lesson 5: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities Exit Ticket (3 points) Draw a tree diagram representing the possible outcomes of flipping a coin and then rolling a six sided die. Based on your outcomes, what is the probability of getting a heads and an even number?