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Thread: Bayes' Theorem

  1. #1
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    Bayes' Theorem

    Cheryl has a collection of 4 red dice and 5 blue dice. She picks one die at random and rolls it 34 times.
    With a red die, the probability of rolling a four is 0.29. With a blue die, the probability of rolling a four is 0.26.
    What is the probability that she used a red die if she gets a four on 6 of the 34 rolls?


    I understand that I have to construct a tree diagram and use conditional probability but I seem to be getting the wrong answer each time I do it. Can anyone help me with steps?
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  2. #2
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    Re: Bayes' Theorem

    Quote Originally Posted by ballerninja29 View Post
    Cheryl has a collection of 4 red dice and 5 blue dice. She picks one die at random and rolls it 34 times.
    With a red die, the probability of rolling a four is 0.29. With a blue die, the probability of rolling a four is 0.26.
    What is the probability that she used a red die if she gets a four on 6 of the 34 rolls?
    I understand that I have to construct a tree diagram and use conditional probability but I seem to be getting the wrong answer each time I do it.
    Whoever set this question is a sadist. I don't think that a tree-diagram is the way to try.
    You are looking for $\mathscr{P}(R|S)=\dfrac{\mathscr{P}(R\cap S)}{\mathscr{P}(S)}$ the probability that she used a red die if she gets a four on 6 of the 34 rolls.

    $\mathscr{P}(S)=\mathscr{P}(S|R)\mathscr{P}(R)+ \mathscr{P}(S|B)\mathscr{P}(B)$

    $\mathscr{P}(S|R)\mathscr{P}(R)= {34\choose 6}(0.29)^6(0.71)^{28}(0.5)$

    Can you finish?
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