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Math Help - i'm stuck

  1. #1
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    i'm stuck

    100 trout are caught in a little lake and returned after they are tagged. Later, another 100 are caught and found to contain 7 tagged trout.
    a) What is the probability of this is the lake conains n trout?
    b) What is your best guess on n?
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  2. #2
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    Quote Originally Posted by wvlilgurl View Post
    100 trout are caught in a little lake and returned after they are tagged. Later, another 100 are caught and found to contain 7 tagged trout.
    a) What is the probability of this is the lake conains n trout?
    b) What is your best guess on n?
    Let X be the random variable number of tagged trout in the second sample.

    a) \Pr(X = 7) = \frac{ {100 \choose 7} \, {n - 100 \choose 100 - 7}}{{n \choose 100}}.

    More generally, if m trout are caught and returned after they are tagged, and k trout are later caught and found to contain x tagged trout:

    \Pr(X = x) = \frac{ {m \choose x} \, {n - m \choose k - x}}{{n \choose k}}.


    b) The best estimate of n is the integer value of n that maximises Pr(X = 7).

    Using technology is the easiest way of finding this value (although it's not difficult to do by hand if you use the right approach).
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