(Q3) 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 :

Number of black balls = x

Total number of balls in the box =

Probability of drawing a black ball =
No. of favourable outcomes
Total no. of outcomes
 =
x
 ....... (1)

When 6 more black balls are placed in the box, number of favourable outcomes to black ball becomes = x + .

Total number of balls in the box becomes = .

Now the probability of drawing a black ball become =
x +
....... (2)

By Problem,

x +
= 2 ×
x
x +
=
x

(x + ) = (x)

x + = x

x - x =

x =

x =

Check :

Equation (1) ----->
x
 =
=
1
Equation (2) ----->
x +
=
=
1
Equation (1) × 2 =
1
 × 2 =
1

and Hence Proved.