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Simulate a Problem and Make an Organized List

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. 1 4. COURSE 3 LESSON 11-6. Simulate a Problem and Make an Organized List.

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Simulate a Problem and Make an Organized List

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  1. 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 . 1 4 COURSE 3 LESSON 11-6 Simulate a Problem and Make an Organized List 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. 11-6

  2. Method 1 Simulate the problem. 100 Spins AC BB CC DB CD CB CA BC AC CC AD DA CB BC CC CD BC BC AA CA CB AD CB DD AB DD BB AB CD BC DC AA DD DB CB DA DB CC DC AD CA CB DB DC CD CB BD DA DD AC 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. COURSE 3 LESSON 11-6 Simulate a Problem and Make an Organized List (continued) 11-6

  3. number of times AA occurs total number of sets P(2 correct guesses) = 2 50 = Substitute. 1 25 Simplify. = 1 25 The experimental probability is , or 4%. COURSE 3 LESSON 11-6 Simulate a Problem and Make an Organized List (continued) The data shows that from 50 test simulations, AA occurs two times. 11-6

  4. 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. COURSE 3 LESSON 11-6 Simulate a Problem and Make an Organized List (continued) The tree diagram shows that out of 16 possible outcomes, there is only one outcome for two correct guesses. 11-6

  5. 1 16 number of times AA occurs total number of possible outcomes P(2 correct guesses) = = 1 16 The theoretical probability is , or 6.25%. 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) 1 4 1 4 = • Substitute. 1 16 = Multiply. This is the same probability you found by making an organized list. COURSE 3 LESSON 11-6 Simulate a Problem and Make an Organized List (continued) 11-6

  6. Sample answer: Assuming that all digits are equally likely, the theoretical probability is . 1 16 COURSE 3 LESSON 11-6 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? 11-6

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