In a terrible game two fair sixsided dice are rolled Your ca

In a terrible game, two fair six-sided dice are rolled: Your can bet On any number 1 through 6. If both dice show your number, you win $2, if exactly one die shows your number you win $0.80 and if neither die shows your number you lose $1. Let X be your winnings from one play. Find EX, i.e. your expected winnings from one play of this terrible game.

Solution

total events = 36

events of both die showing your number = 1 = n(A)

events of either on die showing your number = 5 + 5 =10 = n(B) (Excluding both number are same ).

So,

P( A) = 1/36

P(B) = 10 / 36 =5/18

P(C) = 25 / 36 .

E(x) = P(A) * V(A) + P(B) * V(B) + P(C) * V(C)

E(x) = 1/36 * 2 + 10/36 * 0.8 + 25/36 * (-1) = -5/12 $

So, this game is having expected value of losing 5/12 $ per game.