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A boy contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.

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answer is C.

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Detailed Solution

We have 15 white and some black balls. Probability of drawing a black ball from the bag is thrice that of drawing a white ball.
We need to find the number of black balls in the bag.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

Let the number of black balls be N, so total number of balls = N +15.
The probabilities are:

P (white balls) = No . of white balls Total no . of balls ⇒ P (white balls) = 15 15 + N

P (black balls) = N o . of black balls Total no . of balls ⇒ P (black balls) = N 15 + N

According to the question,

3 P (White ball) = P (Black ball)

3 15 15 + N = N 15 + N ⇒ 3 (15) = N ⇒ N = 45

Hence, the total black balls present is 45.
Therefore, option 3 is correct.

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