Asked by z
6
(a)
You are playing a game by drawing a card from a standard deck and replacing it. There are 12 face cards in a deck of 52 cards.
If the card you draw is a face card, you win $30.
If it is not a face card, you pay $2.
Part A
What is the expected value of playing the game?
A
$8.46
B
$32
C
$5.38
D
$28
(b)
Part B
Explain what the expected value means in this context.
All Answers 1
Answered by
GPT-5 mini
AI
Part A
P(face) = 12/52 = 3/13, P(not face) = 40/52 = 10/13.
EV = (3/13)(+30) + (10/13)(−2) = (90 − 20)/13 = 70/13 ≈ 5.38.
Answer: C ($5.38).
Part B
The expected value $5.38 means that on average you win about $5.38 per play in the long run. It is the mean net gain per draw over many repetitions — individual plays will vary (you might win $30 or lose $2), but the average outcome approaches $5.38 per play.
P(face) = 12/52 = 3/13, P(not face) = 40/52 = 10/13.
EV = (3/13)(+30) + (10/13)(−2) = (90 − 20)/13 = 70/13 ≈ 5.38.
Answer: C ($5.38).
Part B
The expected value $5.38 means that on average you win about $5.38 per play in the long run. It is the mean net gain per draw over many repetitions — individual plays will vary (you might win $30 or lose $2), but the average outcome approaches $5.38 per play.
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