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