The spinner on a wheel of fortune can land with an equal chance on any one of ten regions. Three regions are red, four are blue, two are yellow, and one is green. A player wins $4 if the spinner stops on red and $2 if it stops on green. The player loses $1 if it stops on blue and $5 if it stops on yellow.

What is the expected value rounded to the nearest cent?

Question

The spinner on a wheel of fortune can land with an equal chance on any one of ten regions. Three regions are red, four are blue, two are yellow, and one is green. A player wins $4 if the spinner stops on red and $2 if it stops on green. The player loses $1 if it stops on blue and $5 if it stops on yellow.

What is the expected value rounded to the nearest cent?

anonymous · Answer

The expected value of a spin is $0.00

This is because the expected value of a spin is the probability-weighted average gain/loss per spin, calculated as follows:

$$E(x) = $4(3/10) + $2(0.1) - $1(0.4) - $5(0.2) = 1.2 + 0.2 - 0.4 - 1.0 = 0$$

Hope this helps...