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Math Help - Probability

  1. #1
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    Probability

    Need some help with this problem:

    A nurse is to give Mr. Sean a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Sean will die is 1/3. If he does not get the pill, the probability that he will die is 3/4. Mr. Sean died. What is the probability that the nurse did not forget to give Mr. Sean the pill? What is the probability that Mr. Sean died and the nurse did not give him the pill?

    Thank you!
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  2. #2
    Junior Member atalay's Avatar
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    You should use Bayes' Rule. Therefore, the answer is 1/2.
    Last edited by atalay; April 28th 2010 at 05:29 AM. Reason: wrong answer
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  3. #3
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    Quote Originally Posted by eri123 View Post
    Need some help with this problem:

    A nurse is to give Mr. Sean a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Sean will die is 1/3. If he does not get the pill, the probability that he will die is 3/4. Mr. Sean died. What is the probability that the nurse did not forget to give Mr. Sean the pill? What is the probability that Mr. Sean died and the nurse did not give him the pill?

    Thank you!
    Draw a tree diagram. Then it is easy to see that:

    For the first, it follows from Bayes theorem that Pr(did not forget | died) = \frac{\frac{1}{9}}{\frac{1}{9} + \frac{6}{12} } = .... .

    For the second, (2/3) (3/4) = 6/12.

    Quote Originally Posted by atalay View Post
    You should use Bayes' Rule. Therefore, the answer is 1/2.
    Right idea, wrong answer.
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  4. #4
    Junior Member atalay's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Draw a tree diagram. Then it is easy to see that:

    For the first, it follows from Bayes theorem that Pr(did not forget | died) = \frac{\frac{1}{9}}{\frac{1}{9} + \frac{6}{12} } = .... .

    For the second, (2/3) (3/4) = 6/12.


    Right idea, wrong answer.
    Your answer is 1/2, too.
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  5. #5
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    Quote Originally Posted by atalay View Post
    Your answer is 1/2, too.
    My answer to the second question is 1/2. However, Bayes Theorem is not used for the second question, it is only used for the first.

    By saying use Bayes Theorem and then saying the answer is 1/2, your original reply implied that the answer to the first question is 1/2, which is wrong.
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