# I need help with the below homework question on the expected value.Mark draws one card from a standard deck of 52. He receives $0.35 for a spade, $0.55 for a queen and $0.85 for the queen of...

I need help with the below homework question on the expected value.

Mark draws one card from a standard deck of 52. He receives $0.35 for a spade, $0.55 for a queen and $0.85 for the queen of spades. How much should he pay for one draw to make the game fair?

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### 1 Answer

First, to find the expected value you will need to *multiply the* *probability* of a particular class of card being drawn *by the reward* for drawing it.

The probability of drawing the *Queen of Spades* is 1/52. The benefit is $.85 (.85/1). Multiply across top and bottom of the fractions:

numerator: 1 x .85 = .85

denominator: 52 x 1 = 52

So, you get .85/52. If you do the division, the expected value is $.016. I will wait to round until the end.

The probability of drawing a *Queen* **other than** the Queen of Spades is 3/52. The benefit is $.55.

num: 3 x .55 = 1.65

den: 52 x 1 = 52

1.65/52 = $.032

The probability of drawing a *Spade* **other than** the Queen of Spades is 12/52. The benefit is $.35.

num: 12 x .35 = 4.2

den: 52 x 1 = 52

4.2/52 = $.081

Now add all the expected values together:

.016 + .032 + .081 = .129

Since we are talking about money, we have to round to the nearest cent = $.13

So, to make the game "fair", Mark should pay $.13.