Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $2.
there is no question, just facts
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To find out the expected value (average outcome) of the game for Kyd, we need to calculate the weighted average of all possible outcomes and the probabilities associated with them.
Step 1: Determine the outcomes and their respective probabilities.
- There are 52 cards in a standard deck, and Kyd selects one card.
- There are 12 face cards (Jack, Queen, and King), so the probability of selecting a face card is 12/52 = 3/13.
- There are 40 non-face cards, so the probability of selecting a non-face card is 40/52 = 10/13.
Step 2: Calculate the expected value for Kyd.
- If Kyd selects a face card, North pays him $6. So the outcome is +$6 with a probability of 3/13.
- If Kyd selects a non-face card, Kyd pays North $2. So the outcome is -$2 with a probability of 10/13.
(Expected Value) = (+$6) * (3/13) + (-$2) * (10/13)
(Expected Value) = $18/13 - $20/13
(Expected Value) = -$2/13
The expected value for Kyd in this game is -$2/13, which means on average, Kyd is expected to lose approximately $0.15 per game.