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

Question

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.

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

Bunuel · Accepted Answer

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.

sri30kanth · Answer

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

kungfury42 · Answer

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?

Bunuel · Answer

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.

kungfury42 · Answer

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

Posted from my mobile device

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