Question

In: Math

Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck....

Kyd and North are playing a game. Kyd selects one card from a standard 52-card deck. If Kyd selects a face card (Jack, Queen, or King), North pays him $6. If Kyd selects any other type of card, he pays North $3.

a) What is Kyd's expected value for this game? Round your answer to the nearest cent. $

b) What is North's expected value for this game? Round your answer to the nearest cent. $

Solutions

Expert Solution

P[ Drawing a face card by Kyd ] = number of face cards / total number of cards

P[ Drawing a face card by Kyd ] = 12/52

P[ Drawing a face card by Kyd ] = 3/13

The payoff for Kyd = $6

P[ Drawing other types of cards ] = 40/52

P[ Drawing other types of cards ] = 10/13

The payoff for Kyd = - $3

The expected payoff of Kyd = P[ Drawing a face card by Kyd ]*The payoff for Kyd + P[ Drawing other types of cards ]*The payoff for Kyd

The expected payoff of Kyd = (3/13)*6 + (10/13)*(-3)

The expected payoff of Kyd = 18/13 - 30/13

The expected payoff of Kyd = -12/13

The expected payoff of Kyd = - $0.9231

Loss of $0.9231

The expected payoff of North = P[ Drawing a face card by North ]*The payoff for North + P[ Drawing other types of cards ]*The payoff for North

The expected payoff of North = (3/13)*(-6) + (10/13)*(+3)

The expected payoff of North = - 18/13 + 30/13

The expected payoff of North = 12/13

The expected payoff of North = +$0.9231

Profit of $0.9231


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