Final answer:
Kyd's expected value for the game is approximately -$0.92, indicating an average loss per game, while North's expected value is approximately $0.92, indicating an average gain per game. The options provided do not match these values.
Step-by-step explanation:
To calculate Kyd's expected value (EV), we first need to determine the probabilities of picking a face card versus a non-face card and the associated winnings or losses. There are 12 face cards (Jacks, Queens, Kings) in a standard 52-card deck, and the remaining 40 cards are non-face cards.
The probability of drawing a face card is 12/52, and Kyd would receive $6. The probability of drawing a non-face card is 40/52, and Kyd would pay $3.
The expected value for Kyd is calculated as:
EV = (Probability of face card) x (Winnings with face card) + (Probability of non-face card) x (Loss with non-face card)
EV = (12/52) x 6 + (40/52) x (-3)
EV = (12/52) x 6 + (40/52) x (-3)
EV = (12/52) x 6 - (40/52) x 3
EV = 72/52 - 120/52
EV = -48/52
EV = -$0.9231, rounded to the nearest cent
So, Kyd's expected value for this game is approximately -$0.92, which means Kyd would expect to lose about 92 cents per game on average. As none of the choices (A), (B), (C), or (D) match this value, Kyd's expected value is not listed in one of those options.
The expected value for North is simply the negative of Kyd's expected value since it's a zero-sum game. Therefore, North's expected value is approximately $0.92. Again, this does not match any of the provided choices.