Homework Help: [Statistics] Conditional Probability questions?

1. Feb 8, 2012

KendrickLamar

1. The problem statement, all variables and given/known data

I've attached both the problems into one image to make life easier since problem 1 has a diagram and the other does not.

2. Relevant equations
Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')]
B' = B Complement

3. The attempt at a solution
well for the first one
i dont understand what the P(A|B') is and the .849 is that referring to B'?
SO i did .001(.05) / [(.001(.05)) + P(A|B')(.849)] i dont know what that P(A|B') is so im not sure where to go from there and the answer in the back of the book says .0099

for the 2nd problem
a.) i understand dont need help
b.) i dont know how to get P(AB) given the information provided
c.) well i can get this if i know part b since it would be .4 + .25 - P(AB)

thank u for ur help!

Last edited: Feb 8, 2012
2. Feb 8, 2012

fishshoe

It's not clear where your brackets end in Bayes's Theorem. Try this instead:
P(B|A) = P(A|B) *(P(B))/(P(A))

3. Feb 8, 2012

KendrickLamar

^ that doesn't seem to work, like i'm still not clear on when i'm supposed to use baye's theorem?

ah sorry forgot the final bracket it says this:

Bayes Theorem : P(A|B)P(B) / [P(A|B)P(B) + P(A|B')P(B')]

in the textbook it says that ah well here let me just take a picture of it:

4. Feb 8, 2012

KendrickLamar

also i think the 2nd one the conditional information of .7 is unecessary and it should just be that

P(AB) = P(A)*P(B) = (.4)(.25) = .1?

5. Feb 8, 2012

fishshoe

When you say that P(AB) = P(A) * P(B), you're assuming that the two events are mutually exclusive. But since P(A|B) = 0.7, we know that's not true (otherwise P(A|B) = P(A)). What you want is the probability of A and B (i.e. their intersection).

6. Feb 9, 2012

fishshoe

Also, the version of Bayes' Theorem you're using is more complex than you need to solve the first problem. The basic formula for conditional probability is

$P(B|A) = P(B \cap A)/P(A)$

So you know you're in A because that's given. So you want to know, what's the probability that you'll be in the (tiny) part of A that overlaps with B?