A bag contains X red balls and 5 green balls. 2 balls are picked up from the bag at random, one after the other, without replacement, the probability of both balls being red is 3/7. What will be the value of X?

Explanation

Number of Green Balls = 5. Number of Red balls = X. ⇒ Total number of balls = X + 5. Probability of both balls being red = 3/7 ⇒ x(x – 1)/[(x + 5)(x + 4)] = 3/7 ⇒ 7x² – 7x = 3x² + 27x + 60 ⇒ 4x² – 34x – 60 = 0 ⇒ 2x² – 17x – 30 = 0 ⇒ (2x – 20)(x + 3) = 0 ⇒ x = 10, –3/2. Only 10 satisfies the value of X. ∴ Number of red balls, X = 10.