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Homework Help: [Statistics] Conditional Probability questions?

  1. Feb 8, 2012 #1
    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. jcsd
  3. Feb 8, 2012 #2
    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))
  4. Feb 8, 2012 #3
    ^ 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:
  5. Feb 8, 2012 #4
    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?
  6. Feb 8, 2012 #5
    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).
  7. Feb 9, 2012 #6
    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

    [itex] P(B|A) = P(B \cap A)/P(A)[/itex]

    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?
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