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

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Math Expert
Joined: 02 Sep 2009
Posts: 43804
A student is to take her final exams in three subjects. The probabilit [#permalink]

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08 Dec 2014, 05:19
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Difficulty:

15% (low)

Question Stats:

81% (01:06) correct 19% (01:09) wrong based on 87 sessions

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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

Kudos for a correct solution.

Source: Chili Hot GMAT
[Reveal] Spoiler: OA

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Senior Manager
Joined: 13 Jun 2013
Posts: 278
Re: A student is to take her final exams in three subjects. The probabilit [#permalink]

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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
Manager
Joined: 10 Sep 2014
Posts: 98
Re: A student is to take her final exams in three subjects. The probabilit [#permalink]

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08 Dec 2014, 09:52
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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

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

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29 Mar 2017, 22:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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