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.
- Find the expected value for this game (expected net gain or loss).
- Explain what your calculations indicate about your long-term average profits and losses on this game.
- Should you play this game to win money?
OpenStax Statistics, 4.2 Mean or Expected Value and Standard Deviation, exercise 28