Question

If three prime numbers are randomly selected from the prime numbers less than 30 and no prime number can be chosen more than once, What is the probability that sum of the three prime numbers selected will be even?

A) 10%
B) 27%
C) 30%
D) 36.5%
E) 42%

Answer 1

C) 30%

Explanation:

The sum will be even if one of the primes chosen is even. There is only one even prime of the 10 primes under 30.

There are 9C2 = 36 ways to choose two odd primes from the 9 odd primes under 30, so 36 ways to choose 3 primes whose total is even. There are 10C3 = 120 ways to choose 3 primes, so the probability that 3 randomly chosen primes under 30 will have an even sum is ...

36/120 = 0.30 = 30%