Question

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?

Answer 1

Answer:

$Expected = 0.09375$

Step-by-step explanation:

Given

$Balls = 4$

$n = 4$ --- selection

Required

The expected distinct colored balls

The probability of selecting one of the 4 balls is:

$P = \frac{1}{4}$

The probability of selecting different balls in each selection is:

$Pr = (\frac{1}{4})^n$

Substitute 4 for n

$Pr = (\frac{1}{4})^4$

$Pr = \frac{1}{256}$

The number of arrangement of the 4 balls is:

$Arrangement = 4!$

So, we have:

$Arrangement = 4*3*2*1$

$Arrangement = 24$

The expected number of distinct color is:

$Expected = Arrangement * Pr$

$Expected = 24 * \frac{1}{256}$

$Expected = \frac{3}{32}$

$Expected = 0.09375$