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Back to 4.2 Mean or Expected Value and Standard Deviation

4.2 Exercise 30

Avg difficulty 2.5

A game involves selecting a card from a regular 52-card deck and tossing a coin. The coin is a fair coin and is equally likely to land on heads or tails.

  • If the card is a face card, and the coin lands on Heads, you win $6
  • If the card is a face card, and the coin lands on Tails, you win $2
  • If the card is not a face card, you lose $2, no matter what the coin shows.
  1. Find the expected value for this game (expected net gain or loss).
  2. Explain what your calculations indicate about your long-term average profits and losses on this game.
  3. Should you play this game to win money?

OpenStax Introductory Statistics 2e, 4.2 Mean or Expected Value and Standard Deviation, exercise 30

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Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.