Practice Expected Value in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The expected value of a random variable is the probability-weighted average of all possible outcomes — the long-run mean over many repetitions.
Expected value is what you would "expect" on average after very many trials — not the most likely single outcome, but the center of the distribution.
Example 1
easyA fair six-sided die is rolled. What is the expected value of the outcome?
Example 2
mediumA game costs \5 to play. You win \20 with probability 0.2 and \0$ otherwise. What is the expected profit?
Example 3
mediumA raffle has 100 tickets. One ticket wins \500 and two tickets win \50 each. Each ticket costs \10$. Find the expected net gain per ticket.
Example 4
mediumA prize wheel pays \0, \2, \5, and \20 with probabilities 0.50, 0.30, 0.15, and 0.05, respectively. What is the expected payout per spin?