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A bag contains 24 balls out of which x are white. If one ball is drawn at random the probability of drawing a white ball is y .12 more white balls are added to the bag. Now if a ball is drawn from the bag, the probability of drawing the white ball is $\frac{5}{3} y .$ Find the value of x.

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answer is B.

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Detailed Solution

Given that the bag contains 24 balls of which x are white.
To find the value of x.
Given n(S)=24.
For an event A , the probability of an event P(A) is

P (A) = \frac{Number of favo rable outcomes}{Total number of outcomes}

For case 1:
The probability of drawing white ball is y when total white balls is x.

\Rightarrow P (E) = \frac{n (X)}{n (S)}

\Rightarrow y = \frac{X}{24}

……….(i)
For case 2:
Given 12 more white balls were added.

\Rightarrow P (E') = \frac{n (Y)}{n (S)}

\Rightarrow \frac{5}{3} y = \frac{12 + x}{24 + 12}

\Rightarrow 5 y = \frac{12 + x}{12}

……….(ii)
Substitute y in (i) to (ii),

\Rightarrow 5 \times \frac{x}{24} = \frac{12 + x}{12}

\Rightarrow \frac{5 x}{2} = 12 + x

\Rightarrow 5 x - 2 x = 24

\Rightarrow 3 x = 24

\Rightarrow x = 8

Therefore, the value of x is 8.
Hence, option 2 is the correct answer.

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