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4. 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

4. 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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
Total number of black balls = x Total number of balls = 12 P(E) = (Number of favourable outcomes/ Total number of outcomes) P (getting black balls) = x/12 ——————-(i) Now, when 6 more black balls are added, Total balls become = 18 ∴ Total number of black balls = x+6 Now, P (getting black balls) = (x+6)/18 ——————-(ii) It’s given that, the probability of drawing a black ball now is double of what it was before (ii) = 2 × (i) (x+6)/18 = 2 × (x/12) x + 6 = 3x 2x = 6 ∴ x = 3

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