Found the OE bit complicated than usual probability q approach... so posting another solution which maybe easier to understand for some (who fall in similar category:) )

Set

S consists of all prime integers less than 10. If a number is selected from set

S at random and then another number, not necessarily different, is selected from set

S at random, what is the probability that the sum of these numbers is odd?

*

\frac{1}{8} *

\frac{1}{6} *

\frac{3}{8} *

\frac{1}{2} *

\frac{5}{8} Total ways to choose 2 numbers (repeat doesn't matter): 4x4=16

This would have been 4x3=12 had the Q not mentioned "not necessarily different". I missed that part in the test

Result is odd only when one number is 2 and the other any of the others.

Favorable cases when "2" is the first to be drawn {(2,3),(2,5),(2,7)}=3 , another 3 when "2" is the second to be drawn.

So, probability=(favorable cases/total cases)=6/16=3/8