Question

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

Answer 1

Originally box had 12 balls with x number of red.
Now, box has 18 balls with x+6 numbers of red.
Since the probability has doubled,
p(x+6) = 2 x p(x)

Hence the original number of red balls are 3 out of 12.
And the new numbers of red balls are 9 out of 18.
Original gives you a probability of 0.25
New gives you a probability of 0.5 which is exactly the double and the answer.
In the first case, you know the probably has to be less than 7 red balls, because 7/12 would you give you more than 0.5 which whenever doubled gives you greater than one. So any number above 7 is not possible. The number below 7 which matches the criteria is 3. Hence 3 and 9 are the red balls in the bag (before and after).

Answer 2

Let number of red balls be x

P (red ball) =  x  ÷ 12

If 6 more red balls are added :

The number of red balls = x + 6

P (red ball) =  x + 6  ÷ 18

Since,

x + 6  ÷ 18 = 2 × (x + 12)

x = 3

∴ There are 3 red balls in the bag.