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# 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 - CBSE Class 10 - Mathematics

ConceptProbability - A Theoretical Approach

#### 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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Solution 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 Concept: Probability - A Theoretical Approach.
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