1. ## Probability Help

I got this 2 question that I have being trying to solve for hours but can't seem to figure out.

1- P(A)= 0.71 ; P(B|A)= 0.17 ; P(B|not A)= 0.59 ; P(B)= ?
2- P(B)= 0.27 ; P(A|B)= 0.84 : P(A|not B)= 0.14 ; P(B|A)= ?

Also can explain how to get P(A|not B) and P(B|not A) for future reference?
thank you very much

2. Originally Posted by Panzz
I got this 2 question that I have being trying to solve for hours but can't seem to figure out.

1- P(A)= 0.71 ; P(B|A)= 0.17 ; P(B|not A)= 0.59 ; P(B)= ?
2- P(B)= 0.27 ; P(A|B)= 0.84 : P(A|not B)= 0.14 ; P(B|A)= ?

Also can explain how to get P(A|not B) and P(B|not A) for future reference?
thank you very much
In both cases drawing a tree diagram makes things simple. I'll do 1.

The first two branches are A (0.71) and not A (0.29). The second two branches going from each of the first are B and not B:

Going from A it's B (0.17) and not B (0.83).

Going from not A it's B (0.59) and not B (0.41).

Then Pr(B) = (0.71)(0.17) + (0.29)(0.59) = ....

Pr(A | not B) = (0.71)(0.83)/[(0.71)(0.83) + (0.29)(0.41)] = ....

Pr(not A | not B) = (0.29)(0.41)/[(0.71)(0.83) + (0.29)(0.41)] = ....

The tree diagram makes it all simple and obvious.

Note that for question 2, the first two branches are B and not B. The seocnd two branches are A and not A.