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
REPHRASED 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
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
