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Question
A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a red ball to a blue ball are in the ratio 5 : 2, determine the probability of drawing a blue ball from the bag.
Solution
Let the number of red balls be 8.
Number of blue balls = x
∴ Total number of balls = (8 + x)
∴ `("P"("red ball is drawn"))/("P"("blue bal is draw")) = 5/2`
Let the probability of getting a red ball be A
Favourable number of outcome = 8
∴ p(A) = `8/(8 + x)`
Let probability of getting a blue ball be B
Favourable number of outcome = x
∴ p(B) = `x/(8 + x)`
∴ `("P"("red ball is drawn"))/("P"("blue bal is draw")) = 5/2`
`therefore (8/(8 + x))/(x/(8 + x)) = 5/2`
`=> 8/cancel(8 + x) xx cancel(8 + x)/x = 5/2`
`=> 8/x = 5/2`
∴ 5x = 16
∴ x = `16/5`
∴ P(B) = `x/(8 + x) = (16/5)/(8 + 16/5)`
`= (16/5)/(56/5) = cancel(16)^2/cancel(56)_7`
`= 2/7`
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