In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.

Question

Mathematics

Wendy Schaefer

18 October, 15:29

In a certain card game you draw one card off a standard deck of 52 cards. If you draw a spade you get paid $12, if you draw a red Ace you get paid $20, and if you draw a red Queen you get paid $38. If you draw anything else, you get paid nothing. What should this game cost if it is to be a fair game? Use fractions in your work and then calculate the answer as a decimal rounded to 4 decimal places.

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Answers (1)

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Joshua Sheppard · Answer 1

Step-by-step explanation:

In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades. That leaves 35 cards for everything else.

For the game to be fair, the cost must equal the expected value. The expected value is the sum of each outcome times its probability.

C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)

C = 68/13

C ≈ 5.2308