Expected Value Math Example 2

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Example 2

medium
A game costs \5toplay.Youwin to play. You win \2020 with probability 0.20.2 and \0$ otherwise. What is the expected profit?

Solution

  1. 1
    Set up the expected winnings using the outcomes: win \20withprobability with probability 0.2,win, win \00 with probability 0.80.8.
  2. 2
    Calculate expected winnings: E(W)=20×0.2+0×0.8=4E(W) = 20 \times 0.2 + 0 \times 0.8 = 4
  3. 3
    Subtract the ticket cost to find expected profit: E(profit)=4−5=−1 (expected loss of $1)E(\text{profit}) = 4 - 5 = -1 \text{ (expected loss of } \$1\text{)}

Answer

E(profit)=−$1E(\text{profit}) = -\$1
A negative expected value means the game is unfavorable in the long run. Expected value helps assess whether a gamble or investment is worthwhile.

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.

Learn more about Expected Value →

More Expected Value Examples

Example 1 easy

A fair six-sided die is rolled. What is the expected value of the outcome?

Example 3 medium

A raffle has [formula] tickets. One ticket wins [formula]500[formula][formula] each. Each ticket cos

Example 4 medium

A prize wheel pays [formula]0[formula][formula], [formula]5[formula][formula] with probabilities [fo

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