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

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by M7MBA » Fri Feb 19, 2021 7:31 am

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Difficulty—

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

by Brent@GMATPrepNow » Fri Feb 19, 2021 8:04 pm
M7MBA wrote: ↑
Fri Feb 19, 2021 7:31 am
 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
Brent Hanneson - Creator of GMATPrepNow.com
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