Question

You draw a card from a deck. If it's a king, you win $100. The game costs $2 to play. How much money do you expect to pay?

a. $0
b. $2
c. $98
d. $100

Answer 1

The expected amount of money you will pay to play this game is $5.84.

Step-by-step explanation:

To calculate the expected value, we need to calculate the probability of drawing a king and the amount of money you win. In a standard deck, there are 4 kings out of 52 cards, so the probability of drawing a king is 4/52. If you win $100 for drawing a king, the expected value can be calculated as:

Expected value = (probability of winning * amount won) - (probability of losing * amount lost)

Expected value = (4/52 * $100) - (48/52 * $2)

= $7.69 - $1.85

= $5.84

Therefore, you can expect to pay $5.84 to play this game.