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: x = 3)

Ans:  Random drawing of balls ensures equally likely outcomes

Total number of balls = 12

Total number pf possible outcomes = 12

Number of black balls = x

(1) out of total 12 outcomes, favourable outcomes = x

P (black ball) = Number of favourable outcomes        =  x/12

Total number of possible outcomes

(2) if 6 more black balls are put in the bag, then

The total number of black balls = x + 6

Total number of balls in the bag = 12 + 6 = 18

According to the question

Probability of drawing black ball is second case

= 2 X probability drawing of black ball in first case

x + 6/18 = 2 ( x /12)

x + 6/18 =  x/6

6 x + 36 = 18x x = 3

hence number of black balls = 3