Question

Your friend wants to play a game with a pair of dice. You win if the sum of the top faces is 5, 6, 7, or 8. The winner pays the loser $1 each game. Should you play?

Answer 1

Total number of ways = 36

Number of ways of of getting sum 2 = 1 i.e(1,1)

Number of ways of of getting sum 3 = 2 i.e (1,2) (2,1)

Number of ways of of getting sum 4 = 3 i.e (1,3) (2,2) (3,1)

Number of ways of of getting sum 9 = 4 i.e (4,5) (5,4) (6,3) (3,6)

Number of ways of of getting sum 10 = 3 i.e (6,4) (4,6) (5,5)

Number of ways of of getting sum 11 = 2 i.e (6,5) (5,6)

Number of ways of of getting sum 12 =1 i.e (6,6)

Number of unfavourable cases = 16

Number of favourable cases = 20

Probability of winning $1 = 20/36

Probability of losing $1 = 16/36

E(X) = 1*(20/36) - 1*(16/36) = 1/9

since expected value is positive

we should play the game