Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 On a multiple-choice test, each question has 4 possible answers. You know the answers.

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Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 On a multiple-choice test, each question has 4 possible answers. You know the answers to all but the last two questions on the test. Find the probability of guessing the answers to both questions correctly. Your goal is to find the probability that you will guess the answers to two questions correctly. The probability of guessing correctly for each question is

Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 (continued) Method 1 Simulate the problem. 100 Spins ACBBCCDBCD CBCABCACCC ADDACBBCCC CDBCBCAACA CBADCBDDAB DDBBABCDBC DCAADDDBCB DADBCCDCAD CACBDBDCCD CBBDDADDAC Simulate the problem by spinning a spinner with four equal parts, A, B, C, and D. Let A represent a correct guess and B, C, and D represent an incorrect guess. Two spins represent the last two questions. Simulate 50 tests by spinning the spinner 100 times. Circle the test simulations where you have two A’s. 11-6

Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 (continued) The data shows that from 50 test simulations, AA occurs two times. P(2 correct guesses) = number of times AA occurs total number of sets The experimental probability is, or 4% = 2 50 Substitute. = Simplify

Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 (continued) Method 2 Make an organized list. Make an organized list to find all possible outcomes. The diagram shows one correct guess and three incorrect guesses for each question. The tree diagram shows that out of 16 possible outcomes, there is only one outcome for two correct guesses. 11-6

Simulate a Problem and Make an Organized List COURSE 3 LESSON 11-6 (continued) The theoretical probability is, or 6.25% P(2 correct guesses) = = number of times AA occurs total number of possible outcomes 1 16 The experimental probability of 4% and the theoretical probability of 6.25% are close in value. Check your results. P(2 correct guesses) = P(correct) P(correct) =Multiply This is the same probability you found by making an organized list. = 1414 Substitute

Simulate a Problem and Make an Organized List What is the probability that each of the last four digits of a telephone number is an even number? COURSE 3 LESSON 11-6 Sample answer: Assuming that all digits are equally likely, the theoretical probability is