A bag contains 5 green balls and few blue balls.  If the probability of drawing a blue ball is twice that of drawing a green ball, find the number of blue balls. 

Asked by pdcavita | 4th Dec, 2017, 09:07: PM

Expert Answer:

begin mathsize 16px style Let space the space number space of space blue space balls space be space straight x.
Total space number space of space balls equals 5 space Green space balls space plus space straight x space blue space balls equals 5 plus straight x
Now comma
straight P left parenthesis Green space ball right parenthesis equals fraction numerator 5 over denominator 5 plus straight x end fraction
straight P left parenthesis blue space ball right parenthesis equals fraction numerator straight x over denominator 5 plus straight x end fraction
Given space that comma
straight P left parenthesis blue space ball right parenthesis equals 2 straight P left parenthesis Green space ball right parenthesis
rightwards double arrow fraction numerator straight x over denominator 5 plus straight x end fraction equals 2 open parentheses fraction numerator 5 over denominator 5 plus straight x end fraction close parentheses
rightwards double arrow fraction numerator straight x over denominator 5 plus straight x end fraction equals fraction numerator 10 over denominator 5 plus straight x end fraction
rightwards double arrow 5 straight x plus straight x squared equals 50 plus 10 straight x
rightwards double arrow straight x squared minus 5 straight x minus 50 equals 0
rightwards double arrow straight x squared minus 10 straight x plus 5 straight x minus 50 equals 0
rightwards double arrow straight x left parenthesis straight x minus 10 right parenthesis plus 5 left parenthesis straight x minus 10 right parenthesis equals 0
rightwards double arrow left parenthesis straight x minus 10 right parenthesis left parenthesis straight x plus 5 right parenthesis equals 0
rightwards double arrow straight x equals 10 space or space minus 5
Rejecting space straight x equals negative 5.
Hence comma space number space of space blue space balls equals straight x equals 10 end style

Answered by Rashmi Khot | 5th Dec, 2017, 09:15: AM