Question

A bag comtains 15 ball of which X are blue and the remaining are red . If yhe number of balld are increased by 5, the probability of drawing the red ball doubles, find (1) P(red ball) (2) P (Blue ball) (3) P( Blue ball it of 5 extra ted balls are actually added)

Answer 1

There is  data missing in this question or there is a word missing. It should read "If the number of RED balls are increased by 5, ..."

Total number of balls in the bag = N = 15.
Number of blue balls = X.
Number of red balls = 15 - X.
Probability of drawing a red ball
  = favourable outcomes/total number of outcomes
  = (15 - X)/15

Increase the number of Red balls by 5.
So number of red balls = 15 - X + 5 = 20 - X
Probability of drawing a red ball
   P(Red ball) = (20 - X)/(15+5) = (20 - X)/20

Given    (20 - X)/20 = 2 * (15 - X)/15
             3(20 -X) = 8 (15 - X)
             5 X = 60
               X = 12

So there are 12 blue balls and 3 red balls.  A total of 15 balls.

1) P(red ball) = initial = 3/15 = 1/5. 
           after adding 5 red balls,  2/5

2) P(blue ball) = initial = 12/15 = 4/5. 
           after adding 5 red balls, 12/20 = 3/5

Answer 2

1. 2/5
2.3/5....

hope it helps..