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CBSE Class 10 Answered

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 | 04 Dec, 2017, 09:07: PM
answered-by-expert 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 | 05 Dec, 2017, 09:15: AM
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