Expected Value Statistics Example 4

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

Example 4

medium
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.

Solution

  1. 1
    Step 1: Net outcomes are $16\$16 with probability 0.1, $1\$1 with probability 0.3, and βˆ’$4-\$4 with probability 0.6.
  2. 2
    Step 2: E(X)=16(0.1)+1(0.3)+(βˆ’4)(0.6)=1.6+0.3βˆ’2.4=βˆ’0.5E(X) = 16(0.1) + 1(0.3) + (-4)(0.6) = 1.6 + 0.3 - 2.4 = -0.5.

Answer

E(X)=βˆ’$0.50E(X) = -\$0.50 per play.
Expected value combines each possible net outcome with its probability to estimate the long-run average result. A negative expected value means the game loses money on average for the player.

About Expected Value

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.

Learn more about Expected Value β†’

More Expected Value Examples

Example 1 medium

A game costs [formula]10; otherwise, you win nothing. Find the expected value per game.

Example 2 medium

A raffle sells 200 tickets at [formula]500. Find the expected value for a ticket buyer.

Example 3 medium

A spinner has outcomes: [formula]3 (prob 0.3), $10 (prob 0.2). Find the expected value.

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