1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Smoker Tree Diagram

  1. Dec 6, 2004 #1
    Tree Diagram

    Hello again!

    I'm stuck and need a little push.

    Referring to the diagram: out of a group of smokers, 20% are heavy smokers, 30% are light smokers, and 50% are non-smokers. A light smoker is twice as likely to die as a non-smoker but half as likely as a heavy smoker.

    H: heavy smoker
    L: light smoker
    N: non-smoker
    D: die

    So, I created the tree diagram (see attached) and understand the relationship. I come up with the following.

    [tex]P(D|L)=2P(D|N)=\frac{1}{2}P(D|H)[/tex]

    [tex]P(H|D)=\frac{P(H)P(D|H)}{P(D)}[/tex]

    and likewise for P(L|D) and P(N|D)

    I need to figure out what P(H|D) is given the info and the tree I created.

    Can someone nudge me in the right direction?

    Thanks,
    dogma
     

    Attached Files:

    Last edited: Dec 7, 2004
  2. jcsd
  3. Dec 7, 2004 #2
    waiter...check please

    I think I got it…can someone check me, please?

    The probability of a person being a heavy smoker given that he died:

    [tex]P(H|D)=\frac{P(H \cap D)}{P(D)}=\frac{P(H)P(D|H)}{P(D)}[/tex]

    The probability that a person in this study dies:

    [tex]P(D)=P(H \cap D)+P(L \cap D)+P(N \cap D)[/tex]

    [tex]= P(H)P(D|H)+P(L)P(D|L)+P(N)P(D|N)[/tex]

    …but since [tex] P(D|L)= 2P(D|N)= \frac{1}{2}P(D|H)[/tex]

    …so

    [tex]P(D)= P(H)P(D|H)+\frac{1}{2}P(L)P(D|H)+\frac{1}{4}P(N)P(D|H)[/tex]

    …then

    [tex] P(H|D)=\frac{P(H)P(D|H)}{ P(H)P(D|H)+\frac{1}{2}P(L)P(D|H)+\frac{1}{4}P(N)P(D|H)}[/tex]

    …the P(D|H)'s cancel out leaving a very simple equation to plug and chug

    P(H|D) = 42.1%
     
  4. Dec 10, 2004 #3
    Your answer checks.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Smoker Tree Diagram
  1. Tree diagram problem (Replies: 3)

Loading...