QUESTION

CSAT

Hard

Maths

Prelims 2018

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?

Select an option to attempt

Explanation

The probability of picking a random ball is:

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

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

Black with number 2: $45\%$ of $20 = \frac{9}{20}$ Black with number 3: $30\%$ of $20 = \frac{6}{20}$ 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.