Probabilty help

I am unsure about the following problems, I put what I think the answer is, would appreciate any help. Thanks!


1. For two events A and B, suppose P(A)= .45, P(B)=.75 and P(BlA)= .45
Are A and B independent?

I said no. For them to be independent, P(BlA) would have to equal .75


2. The events A and B are mutually exclusive. If P(A)= .4 and P(B)=.5 what is P(A and B)?

I feel like this might be a trick question? I thought mutually exclusive refered to P(A or B). If it means the same as independent then I answered
P(A and B)=P(A)*P(B)


3. Given P(A and B)= .25, P(A)= .20 and P(A and B)= .30 find P(B)

Just rearranging I got:
P(A or B)= P(A) + P(B) - P(A and B)

P(B) = P(A or B) - P(A) + P(A and B)

Quote:

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Originally Posted by kittysnyde

I am unsure about the following problems, I put what I think the answer is, would appreciate any help. Thanks!


1. For two events A and B, suppose P(A)= .45, P(B)=.75 and P(BlA)= .45
Are A and B independent?

I said no. For them to be independent, P(BlA) would have to equal .75


2. The events A and B are mutually exclusive. If P(A)= .4 and P(B)=.5 what is P(A and B)?

I feel like this might be a trick question? I thought mutually exclusive refered to P(A or B). If it means the same as independent then I answered
P(A and B)=P(A)*P(B)


3. Given P(A and B)= .25, P(A)= .20 and P(A and B)= .30 find P(B)

Just rearranging I got:
P(A or B)= P(A) + P(B) - P(A and B)

P(B) = P(A or B) - P(A) + P(A and B)

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well you have three totaly different answers coming...

1. is correct ...
if you have indep then P(B|A)=P(B)

2. You're wrong here...
Indep and ME are almost opposites
Instead use
HOWEVER, you asked for P(A and B)=P(AB)=0
ME means that the intersection is empty, hence the probability is zero.

3. Doesn't make sense


YOU seem to be mixing up and's (which are intersections) with or's (unions).