- #1
ChickenChakuro
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Homework Statement
Given that P(A|C) > P(B|C) and P(A|[tex]\bar{C}[/tex]) > P(B|[tex]\bar{C}[/tex]), prove that P(A) > P(B)
Homework Equations
How do I write the proof formally?
The Attempt at a Solution
This seems to me intuitively obvious. There are only two sample spaces, either C occurs or does not occur. In both instances, A has a higher chance of ocurrence than B. So how can P(A) NOT be always greater than P(B)? I have been told that P(A) > P(B) can be proven mathematically. However I'm not good at formal proofs. Can anyone help me write this out in mathematical form?
Many thanks!