Question

If you draw a card with a value of four or less from a standard deck of cards, I will pay you $30. If not, you pay me $12. (Aces are considered the highest card in the deck.) Step 2 of 2: If you played this game 704 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

Answer 1

In 704 times there would be a loss of $1623.70.

Number of cards equal to 4 or below = 3 × 4 = 12

Number of cards above 4 = 40

Probability of getting card equal to 4 or less = 12/52 = 0.2308

Probability of getting card more than 4 = 40/52 = 0.7692

Expected value in one draw = Profit - Loss

Expected value in one draw = P(x < 4) × 30 - P(x > 4) × 12

Expected value in one draw =0.2308 × 30 + 0.7692 × 12

Expected value in one draw = 6.924 - 9.2304

Expected value in one draw = - 2.3064

Expected value in 704 times = - 1623.70

In 704 times there would be a loss of $1623.70