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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.
Solution
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.
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