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Question
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag
Solution
Let the number of blue balls be x.
Number of red balls = 5
Total number of balls = x + 5
P (getting a red ball) = 5/(x+5)
P (getting a blue ball) = x/(x+5)
Given that,
`2(5/(x+5)) = x/(x+5)`
10(x+5) = x2 + 5x
x2 - 5x- 50 = 0
x(x-10) + 5(x-10) = 0
(x-10)(x+5) = 0
Either x - 10 =0 or x +5 = 0
x = 10 or x = -5
However, the number of balls cannot be negative.
Hence, number of blue balls = 10
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