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NAME____________ 1. Cds fvde wgryt? A) qrs B) pwr C)xzy

NAME____________ 1. Cds fvde wgryt? A) qrs B) pwr C)xzy 2. Stre hyvf whjut? A) qrs B) pwr C)xzy 3. Hytre de wgryt? A) qrs B) pwr C)xzy 4. Jgrtevde wgryt? A) qrs B) pwr C)xzy 5. Chjoiide wgryt? A) qrs B) pwr C)xzy 6. Ads fvde wgryt? A) qrs B) pwr C)xzy

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NAME____________ 1. Cds fvde wgryt? A) qrs B) pwr C)xzy

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  1. NAME____________ 1. Cds fvde wgryt? A) qrs B) pwr C)xzy 2. Stre hyvf whjut? A) qrs B) pwr C)xzy 3. Hytre de wgryt? A) qrs B) pwr C)xzy 4. Jgrtevde wgryt? A) qrs B) pwr C)xzy 5. Chjoiide wgryt? A) qrs B) pwr C)xzy 6. Ads fvde wgryt? A) qrs B) pwr C)xzy 7. Clwiry tun gryt? A) qrs B) pwr C)xzy 8. Sqrtevde wgryt? A) qrs B) pwr C)xzy 9. Ods fvde wgryt? A) qrs B) pwr C)xzy 10. Xzzyiuhkkgryt? A) qrs B) pwr C)xzy A multiple choice test has 10 questions ….. There are 3 choices for each answer. If you guess every answer, what is the probability that you get 100% correct?

  2. Here are a few of the many possible ways of answering this test: X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

  3. Use the sequential counting principle to count all possible ways of answering the test: Step 1: answer question1 Step 2: answer question2 Step 3: answer question3 Step 10: answer question10 ………………... 3 x 3 x 3 x ……………… x 3 10 = 3 = 59,049 possible ways to fill in the answer sheet

  4. Of the 59,049 possibilities, only 1 is a perfect paper. The probability of guessing everything right is 1/59049 !

  5. NAME____________ 1. Cds fvde wgryt? A) qrs B) pwr C)xzy 2. Stre hyvf whjut? A) qrs B) pwr C)xzy 3. Hytre de wgryt? A) qrs B) pwr C)xzy 4. Jgrtevde wgryt? A) qrs B) pwr C)xzy 5. Chjoiide wgryt? A) qrs B) pwr C)xzy 6. Ads fvde wgryt? A) qrs B) pwr C)xzy 7. Clwiry tun gryt? A) qrs B) pwr C)xzy 8. Sqrtevde wgryt? A) qrs B) pwr C)xzy 9. Ods fvde wgryt? A) qrs B) pwr C)xzy 10. Xzzyiuhkkgryt? A) qrs B) pwr C)xzy Now consider the probability that you guess 7 right and 3 wrong.

  6. First, measure the probability that the first 7 answers are right and the final 3 answers are wrong: # ways to answer the first 7 correctly: 1 # ways to answer question 8 incorrectly: x 2 # ways to answer question 9 incorrectly: x 2 # ways to answer question 10 incorrectly: x 2 The probability that the first 7 answers are right and the final 3 answers are wrong = 8/59049

  7. The probability that the first 7 answers are right and the final 3 answers are wrong = 8/59049 The number of ways of choosing a combination of 7 of the 10 questions to answer correctly = 10 C 7 = 10 x 9 x 8 x 7 x 6 x 5 x 4 = 120 7 x 6 x 5 x 4 x 3 x 2 x 1 The probability of answering 70% of the test correctly = (120) x (8/59049) = 960/59049 = .016...

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