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Question
A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball?
If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.
Solution
Total number of balls = 12
Total number of black balls = x
P (getting a black ball) = `x/12`
If 6 more black balls are put in the box, then
Total number of balls = 12 + 6 = 18
Total number of black balls = x + 6
P (getting a black ball now) = `(x + 6)/18`
According to the condition given in the question,
`2(x/12) - (x+6)/18`
3x = x + 6
2x = 6
x = 3
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