Question

A bag contains 35 balls out of which some are blue. if 7 more blue balls are put in the box and a ball is drawn at random the probability of drawing a blue ball doubles than what it is before. find the number of blue balls in the bag

Answer 1

Answer:

➡️Initially there are 5 blue balls

➡️after adding 7 more balls at last bag have5+7= 12 blue balls.

Solution:

Total balls in bag = 35
Blue balls are = x

Probability of getting a blue ball p(E1) = x/35

Now 7 more blue balls are put in the box:

Total number of blue balls now = (x+7)

Total balls = 35+7= 42

Probability of getting a blue ball p(E2) =(x+7)/42

A.T.Q

2 p(E1) = p(E2)

$2 \times \frac{x}{35} = \frac{x + 7}{42} \\ \\ (2x)(42) = 35(x + 7) \\ \\ 12x = 5(x + 7) \\ \\ 12x = 5x + 35 \\ \\ 12x - 5x = 35 \\ \\ 7x = 35 \\ \\ x = 5$

So, there are 5 blue balls in the bag initially.

Hope it helps you.