Question

A drawer contains red and black balls. When two balls are drawn at random, the probability that they both are red is 1/2. The number of balls in the drawer can be 

(A) 21 

(B) 11 

(C) 4 

(D) 3

Answer 1

Answer is  (A), (C)

Let the drawer contains p balls of which m are red. 

Probability of drawing two red balls at random is

⇒ 1 - 2p + 2p² should be an odd perfect square.

That is, p = 21, 4 but p ≠ 3, when 3 balls out of 4 are red.

Therefore, 15 balls out of 21 are red.