Question
CSATHardPrelims 2018Maths

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?

Explanation

The probability of picking a random ball is:

Red → 1535\frac{15}{35}, and within these 15 red balls:

Red with number 1: 20%20\% of 15=31515 = \frac{3}{15} Red with number 3: 40%40\% of 15=61515 = \frac{6}{15} Black → 2035\frac{20}{35}, and within these 20 black balls:

Black with number 2: 45%45\% of 20=92020 = \frac{9}{20} Black with number 3: 30%30\% of 20=62020 = \frac{6}{20} Now, we need to find the probability of picking either a red ball with number 3 or a black ball with numbers 1 and 2.

Thus, the probability is 47\frac{4}{7}.

Maths PYQs from 2018

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