You are given 1212 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$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.
Added by Jason L.
Step 1
- The probability of drawing a heart on the first card is \( \frac{13}{52} = \frac{1}{4} \). - Since the first card is replaced, the probability of drawing a heart on the second card is also \( \frac{13}{52} = \frac{1}{4} \). - Therefore, the probability of Show more…
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