quasi
Posts:
9,076
Registered:
7/15/05
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Re: probability question about the dice game
Posted:
Feb 14, 2013 12:11 PM
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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
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