Jordan is buying two goldfish the aquarium has 6 solid orange fish and 8 spotted fish. What is the probability that Jordan selects two spotted fish

Answer 1

If you have two events A and B the probability both events happen when they are not independent is:

P(A and B) = P(A) * P(B|A) where P(B|A) is probability event B occurs given event A has occurred.

Let event A be choosing a spotted fish on first selection

Let event B be choosing a spotted fish on the second selection

There are not independent events since we are sampling without replacement.

Since there are 8 spotted fish out of 14 on the first selection:

P(A) = 8/14 = 4/7

After that selection, there will be 13 total fish of which 7 are spotted so:

P(B}A) = 7/13

and P(A and B) = P(A) * P(B|A) = 4/7 * 7/13 = 4/13