Question

A bag contains 6 red balls and some blue balls. If the probability of drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.

Answer 1

let no. of blue balls in the bag be x. then,

acc to question...

Total balls in the bag (X+6)

P (drawing blue ball)=X/(6+X)

P (drawing red ball)=6/(X+6)

now.,..

P(blue)=2 x P (red)

X/(X+6)=2 x 6/(X+6)

x^2+6x=12x+72

x^2-6x-72=0

x^2-12x+6x-72=0

x(x-12)+6(x-12)=0

(x+6)(x-12)=0

=>x=(-6 )or (12)

=>X=12.... (bcoz no. of balls can't be negative).

therefore no. of blue balls is 12.