Question

A worker for Fish and Wildlife wants to estimate the number of trout in a lake. She catches 11 trout, tags them and releases them. If there are a total of 85 trout in the lake, what is the probability that if the worker catches 3 trout, she would catch exactly 1 of the 11 tagged fish (round to at least 4 decimal places)?

Answer 1

To find the probability of catching exactly 1 of the 11 tagged fish out of 3 trout caught, you can use the hypergeometric distribution formula.

Step-by-step explanation:

To find the probability of catching exactly 1 of the 11 tagged fish out of 3 trout caught, we need to use the concept of hypergeometric distribution. The formula for calculating the probability is:

P(X=k) = (C(k,r) * C(n-k,n-r)) / C(n,r)

Where:

P(X=k) is the probability of exactly k successes,

C(n,r) is the number of ways to choose r items from a population of size n, and

C(k,r) is the number of ways to choose exactly k successes from the tagged fish.

Using the formula:

P(X=1) = (C(1,11) * C(2,74)) / C(3,85) = 0.2867

Therefore, the probability that the worker catches exactly 1 of the 11 tagged fish out of 3 trout caught is approximately 0.2867.