Help me find P(A) and P(B)

Hey all!

GIVEN:

P(A|B) = 0.8

P(B|A) = 0.5

P(AuB) = 0.9

The question:

Find P(A) and P(B).

My attempt:

I've done many questions like this, however they have some substantial data in them and it's easy to get the general feel on how to solve them. This question however I cannot solve at all.

My biggest problem is that I do not understand what to do with P(AuB) if I dont know weather P(A) and P(B) are independent events; P(AuB) = P(A)*P(B). How do I solve this without that assumption? I have no laws about it in my book and the three I do have just gets me in a circle and back to nothing. Please help!

Re: Help me find P(A) and P(B)

Use the definition of a conditional probability.

Re: Help me find P(A) and P(B)

P(A|B) = P(AnB)/P(B) ? Then I dont have P(AnB).. and P(AnB) = P(A) + P(B) - P(AuB). Trying many ways I still have three unknowns and two equations. Is there something i've missed? :)

Re: Help me find P(A) and P(B)

Quote:

Originally Posted by

**Hanga** P(A|B) = P(AnB)/P(B) ? Then I dont have P(AnB).. and P(AnB) = P(A) + P(B) - P(AuB). Trying many ways I still have three unknowns and two equations. Is there something i've missed? :)

I agree that something is missing here.

Are you sure that you were asked to find

Could you have been asked to find bounds on those values?

Why not double check the wording?

Re: Help me find P(A) and P(B)

modified, sorry I made a mistake in it, my apologies.

I agree with Plato.

Re: Help me find P(A) and P(B)

The exact wordings are:

For two events A and B we have P(A|B) = 0.8, P(B|A) = 0.5, P(AuB)=0.9

Decide P(A) and P(B).

I'm still trying to figure this out but no dice :(

Re: Help me find P(A) and P(B)

Quote:

Originally Posted by

**Hanga** The exact wordings are:

For two events A and B we have P(A|B) = 0.8, P(B|A) = 0.5, P(AuB)=0.9

Decide P(A) and P(B).

I'm still trying to figure this out but no dice :(

Dice are irrelevant here.

Pr(A) = 0.8 Pr(B) .... (1)

Pr(B) = 0.5 Pr(A) .... (2)

Solve equations (1) and (2) simultaneously for Pr(A) and Pr(B) etc.

Re: Help me find P(A) and P(B)

My attempt (sorry for my previous post):

And whereas and therefore:

If we enter the given information we get:

We know also this formula:

If we enter the given information we get:

and so

Re: Help me find P(A) and P(B)

Quote:

Originally Posted by

**mr fantastic** Dice are irrelevant here.

Pr(A) = 0.8 Pr(B) .... (1)

Pr(B) = 0.5 Pr(A) .... (2)

Solve equations (1) and (2) simultaneously for Pr(A) and Pr(B) etc.

Errr...hemm..

Pr(AnB)=Pr(A|B)Pr(B)=Pr(B|A)Pr(A)

which means you have enough information to determine the ratio of Pr(A) and Pr(B). So Pr(B)=(0.5/0.8)Pr(A)

0.5=Pr(AuB)=Pr(A)+Pr(B)-Pr(AnB)=Pr(A)(1+5/8)-Pr(B|A)Pr(A)

etc

Re: Help me find P(A) and P(B)

I just could not clear my brain enough to see through this problem.

But now I think it is real interesting.

Given then

Re: Help me find P(A) and P(B)

Thank you very much guys! I'm going to study the method today and make sure I understand it perfectly, I belive the key was P(A|B)P(B)=P(B|A)P(A) and some smart moves on your part! :)

Have a nice day!

Re: Help me find P(A) and P(B)

Quote:

Originally Posted by

**CaptainBlack** Errr...hemm..

Pr(AnB)=Pr(A|B)Pr(B)=Pr(B|A)Pr(A)

which means you have enough information to determine the ratio of Pr(A) and Pr(B). So Pr(B)=(0.5/0.8)Pr(A)

0.5=Pr(AuB)=Pr(A)+Pr(B)-Pr(AnB)=Pr(A)(1+5/8)-Pr(B|A)Pr(A)

etc

Yes, I'll have to learn to post only when I'm awake.

Re: Help me find P(A) and P(B)

i too got the same answer....