Pablo plays \(3\) rounds of a game, in which his chances of winning each round are \(\dfrac13, \dfrac16,\) and

[M7MBA]

Pablo plays \(3\) rounds of a game, in which his chances of winning each round are \(\dfrac13, \dfrac16,\) and \(\dfrac1{n},\) respectively. If \(n \ne 0,\) what is the probability that Pablo wins the first two rounds, but loses the third?

A. \(\dfrac1{18n}\)

B. \(\dfrac{n-1}{18n}\)

C. \(\dfrac1{2n}\)

D. \(\dfrac{n+2}{2n}\)

E. \(\dfrac{3n-2}{2n}\)

Answer: B

Source: Manhattan GMAT

[Brent@GMATPrepNow]

Pablo plays \(3\) rounds of a game, in which his chances of winning each round are \(\dfrac13, \dfrac16,\) and \(\dfrac1{n},\) respectively. If \(n \ne 0,\) what is the probability that Pablo wins the first two rounds, but loses the third?

A. \(\dfrac1{18n}\)

B. \(\dfrac{n-1}{18n}\)

C. \(\dfrac1{2n}\)

D. \(\dfrac{n+2}{2n}\)

E. \(\dfrac{3n-2}{2n}\)

Answer: B

Source: Manhattan GMAT

GIVEN:
P(win 1st round) = 1/3
P(win 2nd round) = 1/6
P(win 3rd round) = 1/n, so P(LOSE 3rd round) = 1 - 1/n = n/n - 1/n = (n-1)/n


P(Win - Win - Lose) = P(win 1st round AND win 2nd round AND LOSE 3rd round)
= P(win 1st round) x P(win 2nd round) x P(LOSE 3rd round)
= 1/3 x 1/6 x (n-1)/n
= (n-1)/18n

Answer: B

Cheers,
Brent