Final answer:
The expected value of the game is $0.25, which means option D ($0.50) is the closest answer. The expected value was calculated considering the probabilities of winning and losing, and the respective payouts and costs.
Step-by-step explanation:
The question asks about the expected value of a game where you pay $3.00 to play, and the dealer deals you one card. The payout is $10 if the card is a spade; otherwise, you lose the $3.00 paid to play the game. A standard deck of cards contains 52 cards with 13 cards in each suit, including the spades.
To calculate the expected value, we consider two scenarios. The probability of getting a spade (winning scenario) is 13/52 (since there are 13 spades in a deck of 52 cards). The probability of not getting a spade (losing scenario) is 39/52, as there are 39 cards that are not spades in a standard deck.
The expected value (EV) can be calculated using the formula:
EV = (Probability of winning)×(Winning amount) + (Probability of losing)×(Losing amount)
Thus:
EV = (13/52)×($10) + (39/52)×(-$3)
EV = 0.25×$10 - 0.75×$3
EV = $2.50 - $2.25
EV = $0.25
Therefore, the expected value of playing this game is $0.25, meaning option D ($0.50) is the closest answer after rounding.