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?                (Ans: 3)

Ans: Number of all possible outcomes = 12

Number of outcomes favourable to the event of drawing black ball = x

Required probability =  x/12

Now when 6 more black balls are put in the box, Number of all possible outcomes = 12 + 6 = 18

Number of outcomes favourable to the event of drawing a black ball = x + 6

∴ Probability of drawing a black ball = x + 6 /18

According to the question,

x + 6/18  = 2 ( x/12 )

∴       x = 3