
Re: probability question about the dice game
Posted:
Feb 15, 2013 8:00 AM


quasi wrote: > > 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. > > Then > > P(C) = (p_1)^2 + (p_2)^2 + ... + (p_6)^2 > > Noting that > > p_1 = 1/36 > p_2 = 3/36 > p_3 = 5/36 > p_4 = 7/36 > p_5 = 9/36 > p_6 = 11/36 > > we get > > P(C) = (1/36)^2 + (3/36)^2 + (5/36)^2 + ... + (11/36)^2 > > = (1^2 + 3^2 + 5^2 + ... + 11^2)/36^2 > > = 286/1296 > > hence > > P(A) = (1  (286/1296))/2 > > = 505/1296 > > quasi
Neat! (Or 'cool' as the modern young people say.)  When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

