SOLUTION: Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked. (a) Find the probability of 2 of the 2

Algebra ->  Permutations -> SOLUTION: Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked. (a) Find the probability of 2 of the 2      Log On


   

Question 385348: Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked.
(a) Find the probability of 2 of the 20 fish being marked if the lake has k fish (assuming the fish are caught at random).
(b) What value of k maximizes the probability?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Ten fish are caught in a lake, marked, and then returned to the lake. Two days later 20 fish are again caught, 2 of which have been marked.
(a) Find the probability of 2 of the 20 fish being marked if the lake has k
fish (assuming the fish are caught at random).
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Binomial Problem with n = k and p = 20/k
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P(x = 2) = kC2(20/k)^2*(1-(20/k))^(k-2)
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cheers,
Stan H.