If you draw a card with a value of five or less from a standard deck of cards, I will pay you $49. If not, you pay me $25. (Aces are considered the highest card in the deck.)

Question

Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

There are 52 cards in a deck meaning there are 52 possible cards that you can draw. How many cards (or possibilities) are there for you to get a card of value five or less? These are the cards with values 2, 3, 4 and 5 and since there are four of each of these, there are 16 possible cards you can draw to win the $49. The probability of this is then 16/52.

On the flip side, there are 36 cards you could draw (the remaining cards in the deck), where you have to pay $25. The probability of this is then 36/52.

Thus, the expected value of this proposition is calculated by multiplying the value of winning against the probability of winning and adding it to the value of losing multiplied against the probability of losing:

49*(16/52) + (-25)*(36/52) = -2.23

The expected value is -$2.23.