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# conditional probability

i am having trouble figuring out a conditional probability.  this is what is given:

event a has probability of .47
P(A U B) = .78

What is P(A, given that B has occured) if P(B) = .7

I am having some difficulty getting the intersection here so I can do P(A intersect B)/P(B) in a normal conditional probability.  I have P(B) = .7 so P(A) is obviously not .47 in this case.  P(A) is somewhere between .000000000000001 and .08.  Please help and thank you!
0
JeffreyDurham
1 Solution

Commented:
P(A U B) = P(A) + P(B) - P(A intersect B)
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Commented:
P(A or B) = P(A) + P(B) - P(A and B)
P(A and B) = 1-(P(A)+P(b))
0.47 = 1-(P(A)+0.7)
P(A) = 0.23

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Commented:
jzkidding, your math got messed up a bit, but that's good. We are not permitted to give direct answers to academic types of problems (as this clearly is). Note the answer phoffric gave. It's accurate, but comes nowhere close to giving away homework answers (or whatever this is for). In the future, try to answer this type of question in the same way.

Jeffrey, you should be able to figure it out using phoffric's formula. Don't worry if your answer doesn't match jz's. It shouldn't.
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