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A student is to take her final exams in three subjects. The probabilit

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A student is to take her final exams in three subjects. The probabilit [#permalink]

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Tough and Tricky questions: Probability.



A student is to take her final exams in three subjects. The probability that she will pass the first subject is 3/4, the probability that she will pass the second subject is 2/3, and the probability that she will pass the third subject is 1/2. What is the probability that she will pass at least one of these three exams?

A) 1/4
B) 11/24
C) 17/24
D) 3/4
E) 23/24

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Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Re: A student is to take her final exams in three subjects. The probabilit [#permalink]

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New post 08 Dec 2014, 09:45
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Bunuel wrote:

Tough and Tricky questions: Probability.



A student is to take her final exams in three subjects. The probability that she will pass the first subject is 3/4, the probability that she will pass the second subject is 2/3, and the probability that she will pass the third subject is 1/2. What is the probability that she will pass at least one of these three exams?

A) 1/4
B) 11/24
C) 17/24
D) 3/4
E) 23/24

Kudos for a correct solution.

Source: Chili Hot GMAT


Probability that she will pass in at least one exam = 1- probability that she will fail in all three of her exams.
= 1- \(\frac{1}{4}.\frac{1}{3}.\frac{1}{2}\)
= \(\frac{23}{24}\)
hence E
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Re: A student is to take her final exams in three subjects. The probabilit [#permalink]

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probability of passing at least one = 1 - probability of passing none (or probability of not passing first subject AND not passing second subject AND not passing third subject, so we will have to multiply)

probability of not passing first subject = 1 - (3/4) = 1/4
probability of not passing second subject = 1 - (2/3) = 1/3
probability of not passing third subject = 1 - (1/2) = 1/2

probability of not passing any subjects = (1/4) x (1/3) x (1/2) = 1/24

probability of passing at least one subject = 1 - (1/24) = 23/24

Answer E!
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Re: A student is to take her final exams in three subjects. The probabilit [#permalink]

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New post 29 Mar 2017, 22:03
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Re: A student is to take her final exams in three subjects. The probabilit   [#permalink] 29 Mar 2017, 22:03
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