probability question

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woody_woodpecker

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Jul 14, 2009
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consider two events A and B such that p(A) = 1/4, p(BIA) = 1/2, p (AIB) = 1/4. Which of the following statements are true?

a) A and B are mutually exclusive events
b) p(A^c I B^c) = 3/4
c) p(AIB) + p(AIB^c) = 1



a) mutually exclusive = p(AB) or p(BA) = 0
p(BIA) = p(BA)/p(A)
1/2 = (0) / (1/4)
1/8 not equal to 0 ----> i don't know whether this is true or not, i saw a few examples but still can't figure it out.

while for b) and c), i don't know which formula i need to use. i'm almost totally blank in this topic, i did many questions, but still didn't get used to them.
help me please~
thanks.
 
\(\displaystyle \begin{gathered} P\left( {A^c |B^c } \right) = 1 - P\left( {A|B^c } \right) \hfill \\ P\left( {A|B^c } \right) \ne 1 - P\left( {A|B} \right) \hfill \\ P(BA) = P\left( {B|A} \right)P(A) \hfill \\ \end{gathered}\)
 
woody_woodpecker said:
can you explain a little bit about each of them?
and for which questions are they correspond to?
Click to expand...
I gave you a very strong hint which of the three is the correct answer.
It is not my intent to teach you about conditional probability.
You should have text material on the formulas I gave you.
If you do work through that material then you will understand.
But I am not one of the guys who do other people's homework.
Maybe one of those will come along. Good Luck.
 
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