Question

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 out in the box the probability of drawing a black ball is now double of what it was before. Find $x$.

Answer 1

Total number of balls $=12$

Total number of black balls $=x$

P (getting a black ball) $=x/12$

If 6 more black balls are put in the box, thenTotal number of balls $=12+6=18$

Total number of black balls $=x+6$

P (getting a black ball now) $=x+6/18$

Now,

$2\left(x/12\right)=(x+6/18)$

$3x=x+6$

$2x=6$

$x=3$

$\therefore$ The value of $x$ is $3$.