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A lake contains 200 trout; 50 of them are caught, tagged and returned to the lake.Suppose...

A lake contains 200 trout; 50 of them are caught, tagged and returned to the lake.Suppose we catch 40 trout at random a few days later, what is the probability that 10 ofthem are tagged?

Math   Statistics-And-Probability   
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Answer #1

suppose 10 are tagged can be selected from 50 tagged trout, then remaining 40 - 10 = 30 untagged trout can be selected from 200 - 50  = 150 trout.

And total 40 trout can be selected from 200 trouts.

Therefore if we catch 40 trout at random a few days later then the probability that 10 ofthem are tagged is,

Probability = 0.161331

Note: Above question is a application of Hypergeometric distribution. So, using excel we can find this probability,

Excel Command:

=HYPGEOMDIST(10, 40, 50, 200) = 0.16133141

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