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If two students are chosen at random with replacement from a certain

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If two students are chosen at random with replacement from a certain [#permalink] New post   Updated on: 09 Feb 2022, 02:50
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If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected?

(1) There are 49 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.


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(1) There are 50 male students in the class.
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Originally posted by lexis on 21 Jun 2008, 03:02.
Last edited by Bunuel on 09 Feb 2022, 02:50, edited 1 time in total.
Edited the first statement.
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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   25 Jul 2014, 03:23
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sri30kanth wrote:
If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected?

(1) There are 50 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.

Cartic,

Can you please explain how it is "P(A')=1-P(A)"? Got the correct ans though but unable to understand the approach. Thanks in advance


There are only 4 cases when you are selecting 2 people:
1. (male, male);
2. (female, female);
3. (male, female);
4. (female, male).

The sum of the probabilities of those 4 cases is 1. We need the sum of the probabilities of the first 2 cases: P(1 + 2). The second statement says that the sum of the probabilities of the last 2 cases is 21/50: P(3 + 4) = 21/50. therefore P(1 + 2) = 1 - P(3 + 4) = 1 - 21/50 = 29/50.

Generally, P(x) = 1 - P(not x).

Hope it's clear.
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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   24 Jul 2014, 09:50
Cartic,

Can you please explain how it is "P(A')=1-P(A)"? Got the correct ans though but unable to understand the approach. Thanks in advance
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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   09 Feb 2022, 02:22
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lexis wrote:
If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected?

(1) There are 50 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.

It has been my observation, and correct me if I'm wrong, but on OG questions the information presented in the two options does not contradict. However, here when we take Statement 1 in conjunction with Statement 2, the number of females comes out to be a fraction value which is not feasible. I understand this is irrelevant from solving the question point of view, but it reduces the overall quality of the question. Bunuel can you please check?
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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   09 Feb 2022, 02:53
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kungfury42 wrote:
lexis wrote:
If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected?

(1) There are 50 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.

It has been my observation, and correct me if I'm wrong, but on OG questions the information presented in the two options does not contradict. However, here when we take Statement 1 in conjunction with Statement 2, the number of females comes out to be a fraction value which is not feasible. I understand this is irrelevant from solving the question point of view, but it reduces the overall quality of the question. Bunuel can you please check?


You are right, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. I fixed the first statement so that the statements do not contradict.
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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   09 Feb 2022, 04:20
Bunuel wrote:
kungfury42 wrote:
lexis wrote:
If two students are chosen at random with replacement from a certain class, what is the probability that two male students or two female students are selected?

(1) There are 50 male students in the class.

(2) The probability of selecting one male and one female student is 21/50.

It has been my observation, and correct me if I'm wrong, but on OG questions the information presented in the two options does not contradict. However, here when we take Statement 1 in conjunction with Statement 2, the number of females comes out to be a fraction value which is not feasible. I understand this is irrelevant from solving the question point of view, but it reduces the overall quality of the question. Bunuel can you please check?


You are right, on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. I fixed the first statement so that the statements do not contradict.


Thank you very much Bunuel for your prompt response. Happy with the fix.

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Re: If two students are chosen at random with replacement from a certain [#permalink] New post   14 Sep 2023, 07:07
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Re: If two students are chosen at random with replacement from a certain [#permalink]
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