[Statistics] Conditional Probability questions?

[KendrickLamar]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

well for the first one
i don't 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 don't know what that P(A|B') is so I am 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 don't need help
b.) i don't 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!

 

[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))

 

[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:

 

[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?

 

[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).

 

[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?