# A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a blue ball to a red ball are in the ratio 5 : 2, determine the probability of drawing a blue - Algebra

Sum

A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a blue ball to a red ball are in the ratio 5:2, determine the probability of drawing a blue ball from the bag

#### Solution

Let the number of blue balls be x.

Number of red balls = 8

∴ Total number of balls = (x + 8)

P(blue ball is drawn) = x/(x + 8)

P(red ball is drawn) = 8/(x + 8)

According to the given condition, the probability of drawing a blue ball to a red ball are in the ratio 5:2.

∴ ("P"("blue ball is drawn"))/("P"("red bal is draw")) = 5/2

∴ (x/(x + 8))/(8/(x + 8)) = 5/2

∴ x/(x + 8) = 5/2 xx 8/(x + 8)

∴ x(x + 8) = 20(x + 8)

∴ x2 + 8x = 20x + 160

∴ x2 – 12x – 160 = 0

∴ x2 – 20x + 8x – 160 = 0

∴ x(x – 20) + 8(x – 20) = 0

∴ (x – 20)(x + 8) = 0

∴ x – 20 = 0 or x + 8 = 0

∴ x = 20 or x = – 8

But, number of balls cannot be negative.

∴ x = 20

∴ P(blue ball is drawn) = x/(x + 8)

= 20/(20 + 8)

= 20/28

= 5/7

∴ The probability that a blue ball is drawn from the bag is 5/7.

Concept: Probability of an Event
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