BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

DS problem-

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 49
Joined: Tue Aug 28, 2012 3:47 am
Thanked: 3 times

DS problem-

by amnesty17 » Fri Jun 21, 2013 2:40 am
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
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 2193
Joined: Mon Feb 22, 2010 6:30 pm
Location: Vermont and Boston, MA
Thanked: 1186 times
Followed by:512 members
GMAT Score:770

by David@VeritasPrep » Fri Jun 21, 2013 5:36 am
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.
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Fri Jun 21, 2013 6:16 am
amnesty17 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.
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1