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Question
A bag contains 5 white balls and some blue balls. If the probability of drawing a blue ball is double that of a white ball, determine the number of blue balls in the bag
Solution
Let the number of blue balls be x.
Number of white balls = 5
∴ Total number of balls = (x + 5)
P(blue ball is drawn) = `x/(x + 5)`
P(white ball is drawn) = `5/(x + 5)`
According to the given condition, the probability of drawing a blue ball is double that of a white ball.
∴ P(blue ball is drawn) = 2 × P(white ball is drawn)
∴ `x/(x +5) = 2 xx 5/(x + 5)`
∴ x(x + 5) = 10(x + 5)
∴ x2 + 5x = 10x + 50
∴ x2 – 5x – 50 = 0
∴ x2 – 10x + 5x – 50 = 0
∴ x(x – 10) + 5(x – 10) = 0
∴ (x – 10)(x + 5) = 0
∴ x – 10 = 0 or x + 5 = 0
∴ x = 10 or x = – 5
But, number of balls cannot be negative.
∴ x = 10
∴ The number of blue balls in the bag is 10.
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