DS problem-

[amnesty17]

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.

Could some one solve the problem mathematically for final answer . Is it 4/25 or 29/50?
OA:B

[David@VeritasPrep]

I received a PM on this one...

With a mutually exclusive, complementary data set like this one (the people are either male or female but not both) and if you are selecting two students, you have a simple setup with 3 possibilities. The possibilities are: 2 Males, 1 of each, and 2 Females. Order does not matter so selecting one male and then one female is the same combination as selecting one female and then a male.

So you see you either have one of each (which statement 2 tells you is a 21/50 probability) or you have 2 of something (2 males or 2 females). Since the question does not distinguish between ending up with 2 males or ending up with 2 females you do not need to try to separate these groups. So the probability of EITHER 2 males or 2 females is the COMPLEMENT of the probability of getting one of each. With a complement you just subtract 50/50 - 21/50... So the answer will be 29/50. Of course this is data sufficiency so the answer is simply B.

[Brent@GMATPrepNow]

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.

Target question: what is the probability that two male students or two female students are selected?

Let's rephrase the target question to get . . .

Rephrased target question: What is P(the two students are the same GMAT)?

Statement 1: There are 50 male students in the class.
Since we have no idea how many females are in the class, we cannot answer the target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: The probability of selecting one male and one female student is 21/50.
In other words, P(the two students are not the same GMAT) = 21/50
At this point, we can use the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)

So, P(the two students are the same GMAT) = 1 - P(the two students are not the same GMAT)
We get: P(the two students are the same GMAT) = 1 - 29/50
= 21/50
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent