Question

Question 4
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.

Answer 1

There are 12 balls in the box.
Therefore, total number of outcomes = 12
The number of favourable outcomes = x
Therefore, P (getting a black ball)
$P_1=\frac{x}{12}$

If 6 more balls put in the box, then,
Total number of outcomes = 12 + 6 = 18
And the number of favourable outcomes = x + 6
So, P (getting a black ball)
$P_2=\frac{x+6}{18}$

According to question,
$P_2=2\left(P_1\right)$
$\Rightarrow \frac{x+6}{18}=2\times \frac{x}{12}$
$\Rightarrow 3x=x+6$
$\Rightarrow 2x=6$
$\Rightarrow x=3$