Expected Value Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

A prize wheel pays

\

,

2

\

, and

20

with probabilities

0.50

0.30

0.15

, and

0.05

, respectively. What is the expected payout per spin?

1
Multiply each payout by its probability: $0 \cdot 0.50$ , $2 \cdot 0.30$ , $5 \cdot 0.15$ , and $20 \cdot 0.05$ .
2
Compute each term: $0$ , $0.60$ , $0.75$ , and $1.00$ .
3
Add them: $0 + 0.60 + 0.75 + 1.00 = 2.35$ .

Answer

E(X) = \$2.35

Expected value is a weighted average. It tells you the long-run average payout you would expect if the wheel were spun many times.

About Expected Value

The expected value of a random variable is the probability-weighted average of all possible outcomes — the long-run mean over many repetitions.

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