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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? 

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?  Correct Answer <span class="math-tex">\(\frac{4}{7}\)</span>

Given:

A bag contains 15 red balls and 20 black balls

Calculation:

The winning condition is if the ball is red and numbered 3 or if it is black and numbered 1 and 2

⇒ Total number of balls in bag = 15 + 20 = 35

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

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

⇒ The probability of winning = (6 + 14)/35 = 20/35 = 4/7

∴ The required result will be 4/7.

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