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Probability questions

  1. Jul 27, 2006 #1
    Hey guys, I'm taking a probability course and I'm having some trouble with 2 questions:

    1) Suppose 10% of a company's life insurance policy holders are smokers. The rest are non-smokers. For each non-smoker, the probability of dying during the year is 1% compared to 5% for smokers. Given that a policy holder has died, what is the chance that the policy holder is a smoker?

    Ok, now for this one I had a feeling I should use Bayes' formula. The problem I'm having is assigning variables. This is what I did:

    A1 = {smoker}
    A2 = {non-smoker}
    B1 = {smoker dying}
    B2 = {non-smoker dying}
    C = 10%

    Pr{A1} = 10/100 = .1
    Pr{A2} = 90/100 = .9
    Pr{B1} = 5%
    Pr{B2} = 1%

    I'm not sure if these are even set up right, let alone how to put them into Bayes' formula. Also, how do I write what I am looking for?

    I know that a policy holder died -- The probability that this person was a smoker is 10%. This smoker had a 5% chance of dying during the year.

    I'm really stuck, though...

    The second problem:

    Three missiles, whose probabilities of not hitting a target are 0.3, 0.2, and 0.1, respectively, are fired at a target. Assuming independence, what is the probability that the target is hit by all of the three missiles?

    Now for this problem, I assigned a variable to each missile:

    b1 = {missile 1}
    b2 = {missile 2}
    b3 = {missile 3}


    a1 = {hit target}
    a2 = {not hitting target}


    Pr{b1 | a1} = 0.7
    Pr{b1 | a2} = 0.3

    Pr{b2 | a1} = 0.8
    Pr{b2 | a2} = 0.2

    Pr{b3 | a1} = 0.9
    Pr{b3 | a2} = 0.1

    Now, I think I'm looking for something like Pr(b1 & b2 & b3 | a1). Am I right?

    If so, 0.7 x 0.8 x 0.9 = .504

    Is this correct?

    Thank you for your help.
  2. jcsd
  3. Jul 27, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If the probability of this person being a smoker is 10%, you just answered the question (hint: that's not the answer).

    Try calculating the probability of a smoker dying, and the probability of a non-smoker dying (if you're having trouble, just assume it's a group of ten people).

    Then compare the odds of it being a smoker vs. a non-smoker

    Yes, this one is correct
  4. Jul 28, 2006 #3
    Thanks Office_Shredder.

    So I'm trying to find the probability of a smoker dying. Pr{B1} = 5% isn't that probability?

    I think the probability that a smoker died is: Pr{B1 | A1}


    Probability that a non-smoker died: Pr{B2 | A2}

    Is this the right way of mathematically stating what I am asking? I think the real problem I'm having with all of the Bayes' formula questions is setting up my variables correctly and then finding the corresponding probabilities.
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