# Ex.15.2 Q4 Probability Solution - NCERT Maths Class 10

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## Question

A box contains $$12$$ balls out of which $$x$$ are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If $$6$$ more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find $$x$$.

## Text Solution

What is known?

A box contains  $$12$$balls out of which are black and one ball is drawn at random from the box. If $$6$$ more black balls are put in the box, the probability of drawing a black ball is now double of what it was before.

What is unknown?

The probability that the ball drawn at random will be a black ball and the value of .

Reasoning:

First suppose the number of black balls as .Then find the total number of possible outcomes. Now, find the probability by using the formula

Probability .

Now$$6$$ more balls are put in the box and the probability of drawing a black ball is now double of what it was before,

Now, the probability of drawing a black ball $$= 2 x$$ probability of drawing black ball before.

Step:

Total Number of balls $$= 12$$

Let the number of black balls  $$= x$$

Probability of getting black ball\begin{align} &= \frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes }} \\&=\frac{x}{12}\end{align}

If $$6$$ more black balls are put in the box, the probability of drawing a black ball is now double of what it was before,

Total number of balls $$=\text{ }12+6$$

Number of black balls $$=\text{ }x+\text{ }6$$

Now,

$$2 \times$$ Probability of drawing black ball before $$=$$ probability of drawing black ball.

$$2 \times$$ Probability of drawing black ball before \begin{align}=\frac{\text{ No of possible outcomes }}{\text{ Total no of outcomes}}\end{align}

\begin{align} 2\left( \frac{x}{12} \right)&=\frac{x+6}{18} \\ 2x\,\,\times \,18&=12\left( x+6 \right) \\ 3x&=\,x+6 \\ 3x-x&=\,6 \\ 2x&=\,6 \\ x&=3 \end{align}

Number of black balls are $$3$$

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