Question

Dow has a deck of lo cards numbered 1 through 10. He ia elaning a gome of dalce. drown. He loses 53.50 if an odd numbered card at drowh (a) find the expected walue of playing the gime. Acitis: fite realuce the cacd in the deck exil timen) Whe can eapect bi gan monew. lie can extet to oin bicars per arm. wie tat wapect toflese doll as par dran.

Answer 1

The expected value of the card game is a loss, indicating that over the long term, a player would expect to lose money. Therefore, based on the calculated expected value, one should not play this game with the intent to win money.

Step-by-step explanation:

Expected Value of a Card Game

To calculate the expected value of the game, we need to consider the probability of each outcome and its associated monetary gain or loss. There are 12 face cards (Jacks, Queens, and Kings) and 40 non-face cards in a standard deck of 52 cards. Each face card has two outcomes (heads or tails), and each non-face card has one outcome that results in loss:

• Win $6 if the card is a face card and the coin lands on heads.
• Win $2 if the card is a face card and the coin lands on tails.
• Lose $2 if the card is not a face card.

The expected value is calculated as follows:

(Probability of drawing a face card and getting heads) × (Winnings for this outcome) + (Probability of drawing a face card and getting tails) × (Winnings for this outcome) + (Probability of drawing a non-face card) × (Loss for this outcome)

This results in ($6 × 12/52 × 1/2) + ($2 × 12/52 × 1/2) - ($2 × 40/52). After calculations, the expected value is a loss, indicating that over the long term, a player would expect to lose money.

Therefore, one should not play this game to win money as the expected value suggests that the player would, on average, lose money in the long run.