Question 260011
There are three different kinds of socks in a bag: red, blue, and yellow. The probability of choosing a red sock is 1/5. If there are twice as many blue socks as red socks, what is the probability of choosing a yellow sock?
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{{{1/5}}}th of them are red, {{{2/5}}}ths or them are blue.

That means {{{3/5}}}ths of them are either red or blue, so

the remaining {{{2/5}}} have to be yellow, so the probability
of getting a yellow sock is {{{2/5}}}ths.
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Or you could look at it this way:   

Suppose there are R red socks, B blue socks and Y yellow socks.

Then there are R+B+Y socks in the bag.

Since the probability of getting a red sock is {{{1/5}}},

{{{R/(R+B+Y)=1/5}}}

Cross-multiplying:

{{{5R = R+B+Y}}}

{{{4R = B+Y}}}

Since there are twice as many blue socks as red socks, {{{B = 2R}}}

so if we substitute that:

{{{4R = 2R+Y}}}

{{{2R=Y}}}

So there are twice as many yellow socks as red socks,
so you're twice as likely to select a yellow one as a
red one, so twice {{{1/5}}} is {{{2/5}}}.

Answer: {{{2/5}}}

Checking: There could be just 5 socks in the bag, 1 red ones,
2 blue ones and 2 yellow ones.  There are twice as many blue
ones than red ones, and the probability of getting a red one
is {{{1/5}}}, and the probability of getting a blue one is the
sam as that of getting a yellow one, which is is {{2/5}}}.

Edwin</pre>