How do I show that the probability of it being blue is 5/28 ?

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Answer 1 · 2018-04-17T18:33:53

See below.

We can rewrite the ratio as numbers of each pencil.

#3x# yellow
#2x# blue
#5x# green

If #6# yellow are added, we get:

#3x + 6# yellow
#2x# blue
#5x# green

The probability is given by #"number of yellow"/"total number"#

#(3x + 6)/(3x + 6 + 2x +5x) =3/8#

#(3x+ 6)/(10x + 6) = 3/8#

#8(3x+ 6) = 3(10x + 6)#

#24x + 48 = 30x + 18#

#30 = 6x#

#x =5#

Thus there will be a total of #56# pencils with #2(5) = 10# blue. Thus the probability of picking a blue pencil is #10/56 = 5/28#

As required.

Hopefully this helps!