Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Probability questions
  1. Probability Question (Replies: 2)

  2. Probability question (Replies: 4)

  3. Probability Question (Replies: 21)

  4. Probability Question (Replies: 3)

  5. Probability questions (Replies: 1)