In: Math
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. $
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