Suppose you pay $1.00 to play the following game. A card is drawn from a standard deck. If it is an ace, you recieve $5.00, if it is a king, queen, or jack, you receive $3.00. Otherwise you recieve no money. Find the expected value of your net winning. Use decimal notation for your answer.

Question

Addyson Henderson

Mathematics

3 March, 09:25

Suppose you pay $1.00 to play the following game. A card is drawn from a standard deck. If it is an ace, you recieve $5.00, if it is a king, queen, or jack, you receive $3.00. Otherwise you recieve no money. Find the expected value of your net winning. Use decimal notation for your answer.

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Answers (1)

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Kaylin Ryan · Answer 1

0.08

Step-by-step explanation:

A standard deck contains 52 cards. There are 4 aces and 12 kings/queens/jacks. This means that there is a 4/52 (or 1/13) chance of you winning 5$, and a 12/52 (or 3/13) chance of you winning 3$. To find the expected value, we can simply find the average amount of winnings. This can be done by adding the possible winning values for each card ... Since there is a 1/13 chance that you win 5$, we can add 5*1=5 to the sum. For the kings/jacks/queens, we can add 3*3=9 to the sum. Then, since we win nothing for anything else, we can find the expected value to be 14/13 = 1.08 (approximately). Subtracting the 1$ pay, the expected net winning is 0.08, or 8 cents.