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Math Help - Probability Help!

  1. #1
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    Probability Help!

    Suppose that it is known that in an entrance exam, 10% cheat on the exam, and 90% do not. About 70% of the cheaters get a perfect score, while 20% of the noncheaters get a perfect score.

    1) What is the probability that a randomly selected student taking the exam will get a perfect score?
    2) Give that a student has a perfect score on the exam, what is the conditional probability that it was obtained by cheating?
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  2. #2
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    Quote Originally Posted by rafaeli View Post
    Suppose that it is known that in an entrance exam, 10% cheat on the exam, and 90% do not. About 70% of the cheaters get a perfect score, while 20% of the noncheaters get a perfect score.

    1) What is the probability that a randomly selected student taking the exam will get a perfect score?
    2) Give that a student has a perfect score on the exam, what is the conditional probability that it was obtained by cheating?
    Try drawing a tree diagram to see that:

    1) (0.1)(0.7) + (0.9)(0.2) = ....

    2) (0.1)(0.7)/[(0.1)(0.7) + (0.9)(0.2)] = ....
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