Question

Five individuals from an animal population thought to be near extinction in a certain region have...

Five individuals from an animal population thought to be near extinction in a certain region have been caught, tagged, and released to mix into the population. After they have had an opportunity to mix, a random sample of 10 of these animals is selected. Let X=the number of tagged animals in the second sample. If there are actually 25 animals of this type in the region, what is the probability that:

a) X=2?

b) X<=2?

Math   Statistics-And-Probability   
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Answer #1

Answer:-

Given that:-

If X is the number of S's in a completely random sample of size n drawn from a population consisting of M S's and (N-M) F's Then the probability distribution of X, called the "Hyper geometric distribution", is given by

For x is an integer satisfying max(0,n-N+M)

Here The Given data:-

The parameter values are n= 10 ,M=5(5 tagged animals in the population), and N= 25, So the pmf of X is

a)The probability that exactly two of the animals in the second sample are tagged is

b)The probability that at most two of the animals in the recapture sample are tagged is

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