UPSC Civil Services 2018 Prelims General Studies Paper II

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?