The answer should be E.

Statement 1: We only know the given set contains 2 elements. Nothing about the nature of numbers!! (odd, even ,prime...?)
Statement 2: We know that 2 is not there but we do not know about total elements of the set
Hence 1 and 2 both NOT sufficient

A, B, D eliminated.

Statements 1+ 2: We know there are two elements, 3 is one of them but the other element could be 4(even) or 5 (another prime, odd)!
Not Sufficient

So C is eliminated.

Answer should be E.

karthikpandian19 wrote:A set contains n different positive integers. What is the probability that an integer randomly selected from the set is either prime or even, but not both?

1. n=2
2. 2 is not in the set, while 3 is in the set

statement 1 : INSUFFICIENT
We don't know the 2 integers , so can't find out the probability

Statement 2 : INSUFFICIENT
We don't know how many integers are there in the set.

both statements combined

out of the 2 integers in the set n , one is 3, but we don't know about the other.
if the other were 4, then the probability would have been 1
and if the other were 9, then the probability would have been 1/2

Hence INSUFFICIENT