# The range of possible

• Aug 5th 2012, 10:50 PM
tykim
The range of possible
Conditional probability as below looks simple, but confused for me.

P(A│B)=(P(A∩B))/(P(B))

A. If P(AlB)=0.5, what is the range of possible P(A)?
B. If P(AlB)=0.5, what is the range of possible P(B)?
• Aug 6th 2012, 03:17 AM
Plato
Re: The range of possible
Quote:

Originally Posted by tykim
Conditional probability as below looks simple, but confused for me.
P(A│B)=(P(A∩B))/(P(B))
A. If P(AlB)=0.5, what is the range of possible P(A)?
B. If P(AlB)=0.5, what is the range of possible P(B)?

Here are some useful facts.
$P(A\cap B)=P(A|B)P(B)$

$0\le P(A\cap B)\le P(A)\le 1~\&~0\le P(A\cap B)\le P(B)\le 1$.
• Aug 6th 2012, 03:35 AM
tykim
Re: The range of possible
http://latex.codecogs.com/png.latex?...P(A\cap B)P(B)
Is it correct?

It seems to be P(A│B)=P(A∩B)/P(B)
• Aug 6th 2012, 03:47 AM
Plato
Re: The range of possible
Quote:

Originally Posted by tykim
http://latex.codecogs.com/png.latex?...P(A\cap B)P(B)
Is it correct?

It seems to be P(A\cap B)=P(A|B)P(B)

See my edit.
• Aug 6th 2012, 04:51 PM
tykim
Re: The range of possible
Dear Plato,

0≤P(A∩B)≤P(A)≤1
0≤P(A│B)P(B)≤P(A)≤1
0≤0.5P(B)≤P(A)≤1

I can come to the below. How do you think?

P(B)=0; 0≤P(A)≤1
P(B)=1; 0.5≤P(A)≤1

P(A)=0; P(B)=0
P(A)=1; 0≤P(B)≤1