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Pablo plays 3 rounds of a game, in which his chances of winning each round are

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Pablo plays 3 rounds of a game, in which his chances of winning each round are

by BTGModeratorVI » Tue Jul 07, 2020 6:26 am

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Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/3 ,1/6 , and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?

A. 1/18n
B. (n-1)/18n
C. 1/2n
D. (n+2)/2n
E. (3n-2)/2n

Answer: B
Source: Manhattan prep
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Source: — Data Sufficiency |

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Re: Pablo plays 3 rounds of a game, in which his chances of winning each round are

by Brent@GMATPrepNow » Wed Jul 08, 2020 5:39 am

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BTGModeratorVI wrote: ↑
Tue Jul 07, 2020 6:26 am
 Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/3 ,1/6 , and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?

A. 1/18n
B. (n-1)/18n
C. 1/2n
D. (n+2)/2n
E. (3n-2)/2n

Answer: B
Source: Manhattan prep
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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