starwayinc wrote: > >two players Ann and Bob roll the dice. each rolls twice, Ann >wins if her higher score of the two rolls is higher than Bobs, >other wise Bob wins. please give the analyse about what is the >probability that Ann will win the game
Define events A,B,C by
A = event that Ann's higher score exceeds Bob's.
B = event that Bob's higher score exceeds Ann's.
C = event that the higher scores are equal.
The goal is to find P(A).
By symmetry, P(B) = P(A), hence
P(A) = (1 - P(C))/2
When rolling 2 dice, let p_1, p_2, ..., p_6 be the respective probabilities that higher score is 1,2, ... 6.