A fish tank contains 16 goldfish and 24 guppies. If you randomly select 2 fish, what is the probability that they are both goldfish?

Hello, Shakiya214!

If a fish tank contains 16 goldfish and 24 guppies, then we can deduce that the total number of fish in the tank is: 16 + 24 = 40 fish.
If there are 16 goldfish in the tank, then of the 40 total fish, we have a probability of 16/40.

To illustrate this idea, suppose we had n fish in the tank (a guppies and b goldfish). The probability of selecting any fish is 100% (because there are only fish in the tank). If we had to select the goldfish, we could choose them like this:

p₁, p₂, p₃, p₄ ... pₐ

We could choose any one of these fish twice. This leaves us with: 16/40
Now, if they were NOT replaced, we could simply do it again. Except this time, we can only choose 15 out of the remaining 39 goldfish, leaving us with a probability of: (16/40)(15/39) = 240/1560 = 6/39 = 2/13