Question

A bag contains 18 balls out of which x balls are red. If two more red balls are put in the bag, the probability of drawing a red ball will be `9/8` times the probability of drawing a red ball in the first case. Find the value of x.

Answer 1

Total number of balls = 18.

Number of red balls = x.

Now, total number of balls = 18 + 2 = 20.

Number of red balls now = x + 2.

P(getting a red ball now) =`("Number of favourable outcomes")/"Number of all possible outcomes"`

`= (x+2)/20`

`and P("getting a red ball in first case")= ("Number of favourable outcomes")/"Number of all possible outcomes"`

`= x/18`

Since, it is given that probability of drawing a red ball now will be `9/8` times the probability of drawing a red ball in the first case.

`"Thus", (x+2)/20 = 9/8xx x/18`

⇒ 144(x + 2) = 180x 

⇒ 144x + 288 = 180X 

⇒ 36x = 288 

⇒ `x = 288/36 = 8`

Thus, the value of x is 8.