asadrazanayani

[asadrazanayani]

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I personally like to draw out a diagram, so

Ber..jpg

We have been asked to calculate the P(decline assuming -ve ratio).

The key realization is: P(-ve ratio and decline) = P(decline and -ve ratio)

Now: P(-ve ratio and decline) = P(-ve ratio assuming decline) x P(decline) = P(decline and -ve ratio) = P(decline assuming -ve ratio) x P(-ve ratio)

Therefore: P(-ve ratio assuming decline) x P(decline) = P(decline assuming -ve ratio) x P(-ve ratio)

We can calculate P(-ve ratio) as

P(-ve ratio) = (P(-ve ratio assuming decline) x P(decline)) + (P(-ve ratio assuming not decline) x P(not decline))

We can now replace

P(decline assuming -ve ratio) = (P(-ve ratio assuming decline) x P(decline)) / (P(-ve ratio assuming decline) x P(decline)) + (P(-ve ratio assuming not decline) x P(not decline))

P(decline assuming -ve ratio) = 0.9 x 0.2 / ((0.9 x 0.2) + (0.8 x 0.1))

P(decline assuming -ve ratio) = 0.6923076923

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