If you draw a card with a value of three or less from a standard deck of cards, I will pay you $6. If not, you pay me $5. (Aces are considered the highest card in the deck.) Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Question

Stacy Fitzpatrick

Business

6 September, 10:11

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $6. If not, you pay me $5. (Aces are considered the highest card in the deck.) Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

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Answers (1)

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Beard · Answer 1

Expected value of proposition = - $2.46

Explanation:

A card deck is made up of 52 cards. Assuming Aces of one, two and three are less than three. We will have 12 cards (3 from each of the four signs).

Probability of card of 3 or less = chance of positive outcome/total cards

Probability of a card of 3 or less = 12/52

Probability of drawing a card that is above 3 = 1 - (12/52) = 40/52

Expected value of the proposition = (6*12/52) + (-5*40/52)

Expected value of the proposition = 1.3846 - 3.8462

Expected value of proposition = - $2.4616~-$2.46

This is not a favourable odd and the player will most likely fail to make any profit.