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Question
A box contains some black balls and 30 white balls. If the probability of drawing a black ball is two-fifths of a white ball; find the number of black balls in the box.
Solution
Number of white balls in the bag = 30
Let the number of black balls in the box be x.
∴ Total number of balls = x + 30
P(drawing a black ball) = `x/(x + 30)`
P(drawing a white ball) = `30/(x + 30)`
It is given that, P(drawing a black ball) = `2/5 xx P("drawing a white ball")`
`=> x/(x + 30) = 2/5 xx 30/(x + 30)`
`=> x/(x + 30) = 12/(x + 30)`
`=>` x2 + 30x = 12x + 360
`=>` x2 + 18x – 360 = 0
`=>` x2 + 30x – 12x – 360 = 0
`=>` x(x + 30) – 12(x + 30) = 0
`=>` (x + 30)(x – 12) = 0
`=>` x = –30 or x = 12
Since number of balls cannot be negative, we reject x = –30
`=>` x = 12
Therefore, number of black balls in the box is 12.
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