# * How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1)

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1 Compound probability and predictions Objective: Student will learn counting techniques * Go over HW -Review counting tree -All possible outcomes is called a sample space Go through Problem on P. 12, #2 * How many total outcomes are there if you are rolling two dice? (this is assuming that the dice are different, i.e. 1, 6 isn t the same as a 6, 1) * Have students go through Addition game with dice (w/ partner) One person is odd one person is even The person with the most points wins. * Go through creating a table of values to organize the sample space. * Have students go through Multiplication game with dice (w/partner) What is the theoretical probability of and

2 Probability #5: Counting Games Name Addition Game Rules * Two dice are rolled. * If the sum (add the numbers together) of the number is odd player A scores a point * If the sum of the numbers is even player B scores a point * Roll the dice 36 times and record the results. The person with the most points at the end wins. Odd Even Addition Game Follow-up 1. What was the experimental probability of the following: 2. What was the theoretical probability for each of the following: (For this you will need to identify the total number of outcomes and the total number of odd and even outcomes.) 3. Is this a fair game? Explain. 4. Find the probability of rolling a 7 in the addition game. 5. Find the probability of rolling a number divisible by 3 in the addition game.

3 Homework 1. Find the probability of getting the following results when two number cubes are rolled. a. A sum of 10 b. A sum more than 8 c. A sum of 7 or 11 d. A pair of 5 s 2. Suppose you were to spin the spinner below and then roll a number cube a. Make an organized list of possible outcomes b. What is the probability that you will get a 1 on both the number cube and spinner? c. What is the probability that you will not get a 1 on both the number cube and spinner? d. What is the probability that you will get a 1 on the number cube or the spinner? e. What is the probability that you will get the same number on the number cube and the spinner? f. What is the probability that the sum of the number on the spinner and the number on the number cube will be greater than 8? g. What is the probability that the product of the number on the spinner and the number on the number cube will be 0? 3. Suppose that Ted and Jack did an experiment using the spinner and number cube from question 2. For each trial, they spun the spinner and then rolled the number cube. They got a 1 on both the spinner and the number cube in 4 out of 36 trials. a. Based on the results, what is the experimental probability of getting a 1 on both the number cube and the spinner? b. After comparing the experimental and theoretical probabilities of getting a 1 on both the number cube and spinner, Jack and Ted decided there must be something wrong with the spinner or number cube since the probabilities are not the same. Do you agree? Why or why not?

4 Probability #6: Counting Games Name Multiplication Game Rules * Two dice are rolled. * If the product (multiply the numbers together) of the number is odd player A scores a point * If the product of the numbers is even player B scores a point * Roll the dice 36 times and record the results. The person with the most points at the end wins. Odd Even Multiplication Game Follow-up 1. What was the experimental probability of the following: 2. What was the theoretical probability for each of the following: (For this you will need to identify the total number of outcomes and the total number of odd and even outcomes.) 3. Is this a fair game? Explain.

5 Homework 1. Samira says that if she rolls two number cubes 36 times, she will get a product of 1 exactly once. Lexi says that Samira can t be sure this will happen exactly once, but it will probably happen very few times. Who is right? Explain. 2. Dustin tells Jack that if he rolls two number cubes 100 times, he will never get a product of 32. Ed tells him that he can t be sure. Who is right? Explain your reasoning. 3. Lynda and Matt are trying to decide whether to play a certain game at a carnival. It takes one ticket to play the game. A player flips two plastic bottles. If both bottles land standing up, the player wins ten tickets to use for rides and games. They watch several people play the game and find the following results: i. Both on side: 24 times ii. One standing up and one on side: 14 times iii. Both standing up: 2 times a. Base on the results, what is the probability of winning the game? b. If this game was played 20 times, how many times could you expect to win? c. Wow many tickets would you expect to be ahead or behind by after playing 20 times. Explain. d. Is it possible to find the theoretical probability of winning this game? Why or why not?

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