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.

Answer 1

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`