A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

Given: total balls in the box = 12

Let number of red balls = x

Then probability of drawing a red ball = =

When 6 more red balls are put in the box,

Total balls in the box = 12 + 6 = 18

Red balls in the box = x + 6

Probability of drawing a red ball = =

According to the question, the probability of drawing a red ball when 6 red balls are added = 2(the probability of red ball drawn earlier)

⇒

⇒

⇒ x + 6 = 3x

⇒ 3x – x = 6

⇒ 2x = 6

⇒ x = 3

Thus, there are 3 red balls in the box.