A box contains a yellow ball, an orange ball, a green ball, and a blue ball. Billy randomly selects 4 balls from the box (with replacement). What is the expected value for the number of distinct colored balls Billy will select?

Step-by-step explanation:

Given

--- selection

Required

The expected distinct colored balls

The probability of selecting one of the 4 balls is:

The probability of selecting different balls in each selection is:

Substitute 4 for n

The number of arrangement of the 4 balls is:

So, we have:

The expected number of distinct color is:

step-by-step explanation: