" If the occurrence of B makes A more likely, does the occurrence of A make B more likely?

I guess yes. But I could not figure out the reason. Thanks~~(Wondering)

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- Jun 2nd 2008, 05:29 AMshiningstarpxxA problem come from "Introduction to Probability Models"
" If the occurrence of B makes A more likely, does the occurrence of A make B more likely?

I guess yes. But I could not figure out the reason. Thanks~~(Wondering) - Jun 2nd 2008, 06:13 AMSoroban
Hello, shiningstarpxx!

An interesting question . . .

Quote:

If the occurrence of makes more likely,

does the occurrence of make more likely?

We need Bayes' Theorem: .

We are told that, if happens, is more likely to happen.

. . That is, the probability of , given , is greater than the probability of .

In symbols: .

This means: .

Hence, we have: .

Therefore, the probability of , given , is greater than the probability of

. . The occurence of makes more likely.

- Jun 2nd 2008, 06:14 AMmr fantastic
What you're asking is the following:

Does Pr(A | B) > Pr(A) => Pr(B | A) > Pr(B) ?

The answer is yes. Consider:

.

But it's given that .

Therefore and the implication follows.

**Edit:**Too fast for me*this*time, Soroban. But I like to think our replies ......*complement*each other lol!