Suppose that a student is offered a chance to draw a card from an ordinary deck of 52 playing cards and win $18 for an ace, $8 for a king, and $1 for a queen. If $5 must be paid to play the game, what is the expected loss every time the game is played by the student?
A)expected loss $4.08
B)expected loss $2.92
C)expected loss $5.00
D)expected loss $2.08
E)expected loss $1.77

Question

Suppose that a student is offered a chance to draw a card from an ordinary deck of 52 playing cards and win $18 for an ace, $8 for a king, and $1 for a queen. If $5 must be paid to play the game, what is the expected loss every time the game is played by the student? ​
A)expected loss $4.08
B)expected loss $2.92
C)expected loss $5.00
D)expected loss $2.08
E)expected loss $1.77

Quizplus · Accepted Answer

In order to find the expected loss, we need to multiply the probability of drawing each card by the amount won or lost for each card, and then subtract the cost to play the game.

The probability of drawing an ace is 4/52 (since there are 4 aces in a deck of 52 cards). The probability of drawing a king is also 4/52, and the probability of drawing a queen is 4/52. The probability of drawing any other card is 40/52.

So, the expected winnings for each card are as follows:
- Ace: $18 x (4/52) = $1.38
- King: $8 x (4/52) = $0.62
- Queen: $1 x (4/52) = $0.08
- Other: -$5 x (40/52) = -$3.85

Now we can calculate the expected loss:
Expected loss = ($1.38 + $0.62 + $0.08 - $3.85) - $5
Expected loss = -$0.77

So the expected loss every time the game is played by the student is $0.77 or approximately $0.78. Since we are looking for the answer that is closest to this value, the best choice is B) expected loss $2.92.

Suppose That a Student Is Offered a Chance to Draw