Quant Probability

A bag contains 15 red balls and 20 black balls. Each ball is numbered either 1 or 2 or 3. 20% of the red balls are numbered 1 and 40% of them are numbered 3. Similarly, among the black balls, 45% are numbered 2 and 30% are numbered 3. A boy picks a ball at random. He wins if the ball is red and numbered 3 or if it is black and numbered 1 or 2. What are the chances of his winning?

  1. 1/2
  2. 4/7
  3. 5/9
  4. 12/13

Answer

Total number of balls in the bag = 15 red + 20 black = 35

Winning condition: If the ball is red and numbered 3 or if it is black and numbered 1 or 2

Number of red balls numbered 3 = 40% of 15 = 6

Number of black balls numbered 1 or 2 = 70% of 20 = 14

Probability of winning = (6+14)/35 = 20/35 = 4/7

The correct option is B.