Bill and Larry toss two coins.

Question

Bill and Larry toss two coins. If both coins come up heads, Bill pays Larry $4. Larry pays Bill $1 otherwise.

What is the expected value of this game for Bill?



What is the expected value of this game for Larry?

Answer 1

The possible outcomes are:

 

H, H ;  Bill pays $4  ; Prob= 1/4

 

H, T ; Larry pays $1 ; Prob = 1/4

 

T, H ;  Larry pays $1 ; Prob = 1/4

 

T, T ; Larry pays $1 ; Prob = 1/4

 

Bill will receive $1(3/4)  and will pay out $4(1/4); his expected outcome per game is: .75 - $1 = -$.25

 

Larry will receive $4(1/4) and pay out $1 (3/4);  his expected outcome per game is: $1 - .75 = $.25

 

If the game were played 500 times, on the average, Larry would win $.25 per game!