chetan2u wrote:

What is the probability that the sum of two different single-digit prime numbers will NOT be prime?

(A) 0

(B) \(\frac{1}{2}\)

(C) \(\frac{2}{3}\)

(D) \(\frac{5}{6}\)

(E) 1

Diagnostic # 11

-------CONCEPT------------

Single digit prime numbers are

2,3,5,7

Now, except 2 all are odd so we can only get an odd sum if one of our prime number is even while other is odd (Only an odd number can be prime).

2+3 = 5

2+5 = 7

are only 2 cases to satisfy the condition.

while 2 + 7 = 9, it is not prime

& Now the total cases to get a sum by selecting any 2 prime numbers out of these 4 are 4C2 = 6

So, probability for sum NOT to be prime number = 4/6 = 2/3