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.

Total number of black balls = x

Total number of balls = 12

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

P (getting black balls) \(= \ \frac{x}{12} \) ...... (i)

Now, when 6 more black balls are added,

Total balls become = 18

\(\therefore \) Total number of black balls = x + 6

Now, P (getting black balls) \( = \ \frac{x \ + \ 6}{18} \) ....... (ii)

Solving equation (i) and (ii)

x = 3