Question

It costs $7.00 to play a very simple game in which a dealer gives you one card from a deck of 52 cards. if the card is a heart, spade, or diamond, you lose. if the card is a club other than the queen of clubs, you win $11.50. if the card is the queen of clubs, you win $50.00. the random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. what is the mean of x, rounded to the nearest penny?

a. $3.38
b. −$3.62
c. −$3.38
d. $3.62

Answer 1

It costs $7.00 to play a straightforward game in which a dealer gives you one card from a deck of 52 cards.

If the card is a heart, spade, or diamond, you lose.

If the card is a club other than the queen of clubs, you win $11.50.

If the card is the queen of clubs, you win $50.00.

The random variable x represents your net gain from playing this game once, or your winnings minus the cost to play. What is the mean of x, rounded to the nearest penny?

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Random "winnings"::.....-7.......4.50......43

Probabilities::........ 39/52....12/52....1/52

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u(x) = [39*-7 + 12*4.5 + 43]/52 = -$3.38