Given P(A)=.45, P(B)=.31 calculate:
P(A|B)

P(B|A)

I do not know the source of this problem.  I'm simply trying 
to find help for a friend.  She was having trouble with 4 
problems that she was trying to understand.  I told her about 
the wonderful online math resources that are available.  Thank
 you for any help in helping her understand these types of 
problems.

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P(A|B) means "the probability that A is true if you 
are GIVEN that B is true".

You must be given P(A&B), the probability that both A and B
are true at the same time in order to calculate P(A|B) or 
P(B|A)

The formulas are

          P(A&B)                   P(A&B)
P(A|B) = ————————    and P(B|A) = ————————
           P(B)                     P(A)

If you had, say P(A)=.45, P(B)=.31 and P(A&B) were, say, .2, 
then you could calculate

P(A|B) = .2/.31 = .6451612903

P(B|A) = .2/.45 = .4444444444  

But without P(A&B) you cannot calculate these.

Edwin
AnlytcPhil@aol.com