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You draw a card from a 52-card deck and replace it. A face card (12 of the 52 cards) wins $30; any other card costs $2. What is the expected value of playing this game once?
AAbout -$2.00
BAbout $30.00
CAbout $0.00
DAbout $5.38
Answer & Solution
Correct answer: D. About $5.38
1. P(face card) = 12/52 and P(not a face card) = 40/52.
2. Expected value = (30)(12/52) + (-2)(40/52) = 360/52 - 80/52 = 280/52.
3. 280/52 ≈ 5.38, so the expected value of the game is about $5.38.
4. Option A only reflects the loss branch and option C only the win amount, so neither accounts for both weighted outcomes.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.2 Mean or Expected Value and Standard Deviation_
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