# 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?

cburr | Middle School Teacher | (Level 2) Associate Educator

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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.