Probabilty help

• Dec 10th 2009, 08:59 PM
kittysnyde
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)
• Dec 11th 2009, 12:21 AM
matheagle
Quote:

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)

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 $P(A\cup B)=P(A)+P(B)-P(AB)=P(A)+P(B)$
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
$.25\ne.3$

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