WDYE? 2.3: Designing a Fair Game Learning Target: I will analyze the fairness of a game by listing all possible outcomes in a tree diagram and determining theoretical probabilities. HW: 1) Get a parent signature on WDYE packet #1 2)Complete the WDYE Investigation 2-3 p. 4 and Correct with the Zaption video: WDYE Warm Up: Show ALL work with Proper notation!! A bag contains marbles: 3 red, 7 blue, and 6 yellow. What is the probability of drawing a marble that is not red? What is the probability of drawing a marble that is either red or blue?

Warm-Up Question Show ALL work with Proper notation!! A bag contains 3 red marbles, 7 blue marbles, & 6 yellow marbles. – What is the probability of drawing a marble that is not red? – What is the probability of drawing a marble that is either red or blue? P(not red) = 1 – P(red) = 1 - 3/16 = 13/16 P(R or B) = P(Red) + P (Blue) = 3/16 + 7/16 = 10/16 = 5/8

Inv. 2-3 packet p. 2

Tossing Three Coins Events: Start A _____diagram is an illustration using branches to show the sample space of an event. The ________ space is another name for the set of possible outcomes of an event. tree diagram sample space

Teacher note for previous slide: Model how to make this tree diagram on the board and students copy in packet. Events: Start

1.The sample space for tossing three coins is the list of all possible outcomes. {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} 2.There are 8 possible outcomes, and they are all equally likely.

P (3 coins match) = 2/8 or 1/4 P (exactly 2 coins match) = 6/8 or 3/4 No, this is not a fair game. Tevy has more chances to score a point (2 coins match), so he is more likely to win.

You would expect exactly 2 coins to match ¾ of the time. ¾ of 24 = 18 P (exactly 2 coins match) = 18/24 trials Santo means that all 3 coins match sometimes. Tevy is saying the probability is less than ½. If time, model building another tree diagram. X 3 (Hint: Write a proportion.)

Teacher note: Virtual nerd video example slides Challenge slides (no answers) slides 14-15

1.What is the probability of not wearing a red shirt? (Blue, Purple, Red) (Jeans, Skirt) (Sandals, High Heels) P(not R) = 1- P(R) = 1 – 1/3 = 2/3 P(not R) = P(P + B) = 1/3 +1/3 = 2/3 OR X

What is the probability of wearing an outfit with jeans and sandals? (Blue, Purple, Red) (Jeans, Skirt) (Sandals, High Heels) P(J and S) = 3/12 = 1/4

What is the probability of wearing either a purple or blue shirt? (Blue, Purple, Red) (Jeans, Skirt) (Sandals, High Heels) P(P and B) = 1/3 + 1/3 = 2/3

Challenge: Karen and Mia invent another game. They roll a number cube twice and read the digits shown as a two- digit number. So, if Karen gets a 6 and a 2, she has 62. Create a tree diagram for this situation. List all of the possible outcomes. Events: Start

Challenge: Karen and Mia invent another game. They roll a number cube twice and read the digits shown as a two- digit number. So, if Karen gets a 6 and a 2, she has 62. Create a tree diagram for this situation. List all of the possible outcomes. Events: Start

b. What are all of the possible outcomes when you roll a number cube twice and create a two-digit number? c. What is the least number possible? d. What is the greatest number possible? e. Are all numbers equally likely? f. Suppose Karen wins on any prime number and Mia wins on any multiple of 4. Explain how to decide who is more likely to win.

WDYE? 2.3: Designing a Fair Game Did I reach my Learning Target? I will analyze the fairness of a game by listing all possible outcomes in a tree diagram and determining theoretical probabilities. HW: Complete the WDYE Investigation 2-3 p. 4 and Correct with the Zaption video: WDYE 2.3