Problem Solving

While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?

A. 1/2
B. 17/36
C. 91/216
D. 11/36
E. 25/216

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

M7MBA wrote:While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?

A. 1/2
B. 17/36
C. 91/216
D. 11/36
E. 25/216

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

The possible results of the two dice = 6*6 = 36

Favourable cases of sum 7 = (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6 cases

Probability of him winning in each throw = 6/36 = 1/6

i,.e. Probability of him not winning in each throw = 1-(1/6) = 5/6)

One chance includes three throws

Probability of winning ina chance = 1- (probability of not winning in a chance i.e. three throws) = 1-(5/6)*(5/6)*(5/6) = 1- (125/216) = 91/216

Answer: Option C