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Math Help - Geometric Distribution Question

  1. #1
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    Geometric Distribution Question

    In the process of meiosis, a single parent diploid cell goes through eight different phases. However, only 60% of the processes pass the first six phases and only 40% pass all eight. Assume the results from each phase are independent.


    (a) If the probability of a successful pass of each one of the first six phases is constant, what is the probability of a successful pass of a single one of these phases?

    (b) If the probability of a successful pass of each one of the last two phases is constant, what is the probability of a successful pass of a single one of these phases?


    I am not 100% sure this is a geometric distribution, but I am not sure how to set up the formula. Thanks for any help.
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  2. #2
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    Hello Oblivionwarrior
    Quote Originally Posted by Oblivionwarrior View Post
    In the process of meiosis, a single parent diploid cell goes through eight different phases. However, only 60% of the processes pass the first six phases and only 40% pass all eight. Assume the results from each phase are independent.


    (a) If the probability of a successful pass of each one of the first six phases is constant, what is the probability of a successful pass of a single one of these phases?

    (b) If the probability of a successful pass of each one of the last two phases is constant, what is the probability of a successful pass of a single one of these phases?

    I am not 100% sure this is a geometric distribution, but I am not sure how to set up the formula. Thanks for any help.
    (a) If the probability of a successful pass of each one of the first six phases is x, and the results are independent, then the probability that all six phases are passed is x^6 = 0.6

     \Rightarrow x= \sqrt[6]{0.6}=0.9184 (to 4 d.p.)

    (b) If the probability of a successful pass of each one of the last two phases is y, then the probability that both of these are passed is y^2. So:

    x^6y^2=0.4

    \Rightarrow y^2=\frac{0.4}{0.6}

    \Rightarrow y = \sqrt{\frac23}=0.8165 (to 4 d.p.)

    Grandad
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