In the game of "Hearts," two cards are drawn at random without replacement from a
standard 52-card deck. If neither card is a heart, you win nothing and must pay $7. If
exactly one of the two cards is a heart, you win $7. If both cards are hearts, you win
$17. What is the expected value of this game from the perspective of the player?
Round your answer to the nearest cent (two decimal places). Do not include the $ in
your answer.
To help answer this question, construct an expected value table like the one below
where the random variable X represents the net result of playing.
a (net
result)
Description
17
Two hearts
156
2652
7
One
heart
39
-7
No hearts
1482
2652
P(x)
Hint: For the case where exactly one of the cards is a heart, you must add the probabilities
of the two scenarios where the first card is a heart and the second is not, or the first card is
not a heart and the second is. Remember that the sum of the probabilities of a discrete
probability distribution function must be 1.

In the game of Hearts two cards are drawn at random without replacement from a standard 52card deck If neither card is a heart you win nothing and must pay 7 If class=