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

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Bunuel
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A student is to take her final exams in three subjects. The probabilit [#permalink] New post   08 Dec 2014, 06:19
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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
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E
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Re: A student is to take her final exams in three subjects. The probabilit [#permalink] New post   08 Dec 2014, 10:45
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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] New post   08 Dec 2014, 10:52
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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] New post   13 Feb 2021, 07:13
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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.


Solution:

The probability that the student will pass at least one of these three exams is 1 minus the probability that she will not pass any of the three exams, i.e., she fails all 3 exams. Therefore,

P(passes at least one exam) = 1 - P(fail all 3 exams)

= 1 - (1 - 3/4)(1 - 2/3)(1 - 1/2)

= 1 - 1/4 x 1/3 x 1/2 = 1 - 1/24 = 23/24

Answer: E
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gmatclubot
Re: A student is to take her final exams in three subjects. The probabilit [#permalink]
13 Feb 2021, 07:13
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