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Here are a sequence of deductions I saw in a textbook; given that:

x + y = 1 (x and y are probabilities)

here we go...

1) 0.1x + 0.6y = x

0.9x + 0.4y = y

so therefore

2) x = 0.6/0.9 y

x = 2/3 y

so therefore

3) x = 1 - y

x = 2/3 y

so therefore

4) x = 2/5

y = 3/5

My problem is - I can't understand how the author went from 3) to 4). Now don't get me wrong, I can understand it logically; thinking it over in my head;

IF x = 2/3 y

THEN it must be that y = 1.5x

so 4) makes sense because 3/5 = 1.5 * 2/5

However I just can't figure out what he did with the equations from 3) in order to get those numbers (3/5 and 2/5)

1 Answers 1

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You have $\text{I}\,\,\,\,x=1-y$$\text{II}\,\,\,\,x=\frac{2}{3}y$

Thus, substituting II into I you get $\frac{2}{3}y=1-y\Longrightarrow \frac{5}{3}y=1\Longrightarrow y=\frac{3}{5}$ and thus also $ \text{II}\,\,\,x=\frac{2}{3}\frac{3}{5}=\frac{2}{5}$

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    D'oh! Seems so obvious now. Thanks!2012-05-31