Risk Math Example 3

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

Example 3

easy
A lottery ticket costs \2 and pays \1,000,000 with probability 12,000,000\frac{1}{2,000,000}. Calculate the expected value and determine whether this is a good financial decision.

Solution

  1. 1
    Expected winnings: E = \frac{1}{2,000,000} \times 1,000,000 = \0.50$
  2. 2
    Net expected value: \0.50 - \2.00 = -\1.50$ (expected loss)
  3. 3
    Conclusion: on average, you lose \$1.50 per ticket β€” a poor financial investment

Answer

Expected value = -\1.50$ per ticket. Lotteries are financially unfavorable on average.
Lotteries always have negative expected value for participants β€” that's how they generate revenue. Despite this, people buy tickets for entertainment value or for the small chance at life-changing wealth. Understanding EV separates financial logic from emotional appeal.

About Risk

Risk is the possibility of loss or negative outcome, quantified by combining the probability of the event with the severity of its impact: Expected Loss = P(loss) times amount of loss.

Learn more about Risk β†’

More Risk Examples

Example 1 medium

A business faces two possible disasters: (A) equipment failure β€” probability 0.10, cost [formula]500

Example 2 hard

Should you buy insurance for [formula]5000 loss occurring with probability 0.03? Calculate expected

Example 4 hard

Two investment options: A = certain gain of [formula]1000, 40% chance of $0. Calculate EV for both.

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