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प्रश्न
A bag contains 12 blue balls and x red balls. If one ball is drawn at random if 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that it will be a red ball, then find x.
उत्तर
Sample space = 12 + x
n(S) = x + 12
8 more red balls are added
Sample space = x + 12 + 8 = x + 20
Number of red balls = x + 8
Probability of drawing red ball = `(x + 8)/(x + 20)`
By the given condition
`(x + 8)/(x + 20) = 2(x/(x + 12))`
(x + 8)(x + 12) = 2x(x + 20)
x2 + 20x + 96 = 2x2 + 40x
x2 + 20x – 96 = 0
(x + 24)(x – 4) = 0
x = − 24 or x = 4
The value of x = 4 ...(Number of balls will not be negative)
The probability of getting red balls = `(x/(x + 12))`
= `4/16`
= `1/4`
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