Expected Value Math Example 3

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Example 3

medium
A raffle has 100100 tickets. One ticket wins \500andtwoticketswin and two tickets win \5050 each. Each ticket costs \10$. Find the expected net gain per ticket.

Solution

  1. 1
    Expected winnings: E(W)=1100(500)+2100(50)+97100(0)=5+1+0=6E(W) = \frac{1}{100}(500) + \frac{2}{100}(50) + \frac{97}{100}(0) = 5 + 1 + 0 = 6.
  2. 2
    Expected net gain: E=6โˆ’10=โˆ’4E = 6 - 10 = -4.

Answer

E=โˆ’$4E = -\$4
The expected net gain accounts for the ticket cost. A negative value indicates a net loss on average, which is typical for raffles and lotteries.

About Expected Value

The expected value of a random variable is the probability-weighted average of all possible outcomes โ€” the long-run mean over many repetitions.

Learn more about Expected Value โ†’

More Expected Value Examples

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Example 4 medium

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