Practice Expected Value in Statistics

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 long-run average outcome of a random process, calculated as the weighted sum of each possible outcome times its probability. It represents what you would earn or lose on average per trial if the process were repeated infinitely many times.

If you played a game forever, expected value is your average result per play. Positive EV = profitable long-term. Negative EV = you'll lose over time. It's the mathematical way to evaluate risky decisions.

Example 1

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A game costs \2 to play. You roll a fair die: if you roll a 6, you win \10; otherwise, you win nothing. Find the expected value per game.

Example 2

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A raffle sells 200 tickets at \5 each. There is one prize of \500. Find the expected value for a ticket buyer.

Example 3

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A spinner has outcomes: \1 (prob 0.5), \3 (prob 0.3), \$10 (prob 0.2). Find the expected value.

Example 4

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A game costs \4 to play. You win \20 with probability 0.1, \5 with probability 0.3, and \0 otherwise. Find the expected net value of one play.
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