Expected Value Statistics Example 2

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

Example 2

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

Solution

  1. 1
    Step 1: P(win)=1200P(\text{win}) = \frac{1}{200}, net gain = 500โˆ’5=$495500 - 5 = \$495.
  2. 2
    Step 2: P(lose)=199200P(\text{lose}) = \frac{199}{200}, net gain = โˆ’$5-\$5.
  3. 3
    Step 3: E(X)=1200(495)+199200(โˆ’5)=2.475โˆ’4.975=โˆ’$2.50E(X) = \frac{1}{200}(495) + \frac{199}{200}(-5) = 2.475 - 4.975 = -\$2.50.

Answer

E(X)=โˆ’$2.50E(X) = -\$2.50 per ticket.
The negative expected value confirms the raffle organiser profits on average. The total collected is \1000 (200 ร— \5) but only \500 is given as a prize, so the organiser expects to keep \500.

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 โ†’

More Expected Value Examples

Example 1 medium

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

Example 3 medium

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

Example 4 medium

A game costs [formula]20 with probability 0.1, [formula]0 otherwise. Find the expected net value of

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