Find the expected value.
-You are given 12 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn).
This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to
You)of the game. Round to the nearest cent.

Question

Quizplus · Accepted Answer

The probability of drawing a heart from a standard deck of 52 cards is 1/4 (since there are 13 hearts out of 52 cards). Since the drawing is with replacement, the probability of drawing two hearts in a row is (1/4) * (1/4) = 1/16. The probability of not drawing two hearts is therefore 1 - 1/16 = 15/16. The expected value (EV) is calculated as: EV = (Probability of winning * Amount won) + (Probability of losing * Amount lost) = (1/16 * $12) + (15/16 * -$1) = $0.75 - $0.9375 = -$0.1875, which rounds to -$0.19.

Find the Expected Value