4. 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.

Answers (1)

Total number of balls in the bag = 12

Number of black balls in the bag = x

\therefore P(getting\ a\ black\ ball) = \frac{x}{12}

According to the question,

6 more black balls are added to the bag.

\therefore Total number of balls = 12 + 6 = 18

And, the new number of black balls = x+ 6

\therefore P'(getting\ a\ black\ ball) = \frac{x+6}{18}

Also, P' = 2\times P

\implies \frac{x+6}{18} = 2\left (\frac{x}{12} \right )

\\ \implies \frac{x+6}{18} = \frac{x}{6} \\ \implies x+6 = 3x \\ \implies 2x = 6

\implies x =3

The required value of xis 3