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Math Help - Probability modelling

  1. #1
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    Probability modelling

    Wassup guys.

    I have this pain of a math problem that I need help with. There's this question:

    "Suppose that the probability of a parent having no offspring is 1/4, and the probability of the parent having two offspring is 3/4. What's the probability that the population will die out in the 4th generation?"

    The lecturer insists that there are no errors in the question, grammatical or otherwise.

    Help anyone?
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  2. #2
    MHF Contributor
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    Re: Probability modelling

    work out the probability of the 3rd generation containing 1,2,3,... pairs of adults.

    Let the number of pairs of adults in generation 3 be X.
    Let the size of generation 4 be Y.

    Use this identity: P(y=0) = P(y=0 and x=1) + P(y=0 and x=2) + p (y=0 and x=3) ..... up to the maximum possible value of x.

    Check you understand why this works.
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  3. #3
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    Re: Probability modelling

    Another friend gave me the idea of bacteria, where the birthing process (mitosis) would always yield two offspring, in which case we simply construct a 4-step transition matrix with the states "0" and "1" being "no offpring" and "two offsrping" respectively, then we find P^4(10)...what do you think?
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