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

Total probability with different probabilities

  1. Apr 13, 2009 #1

    Pengwuino

    User Avatar
    Gold Member

    I have a silly question that has actually been kinda racking my brain since I have almost no formal education when it comes to probabilities. Let's say I know that a girl has a 40% chance of earning a college degree. Let's also say that right handed people have a 30% chance of earning a college degree. Then let's keep tossing in things like california girls have a 50% chance of getting a college degree. Obviously you can keep finding characteristics of that girl and find the statistics behind their success in getting a college degree.

    Now the grand question is... what is the probability that a californian, right-handed, girl has of getting a college degree? I assume we can't simply multiply probabilities because it seems like you can keep throwing probabilities out like that and eventually make the probability nearly 0 even though it can't be...
     
    Pengwuino, Apr 13, 2009
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Apr 14, 2009 #2

    mXSCNT

    User Avatar

    A = person goes to college, B = person is female, C = person is right-handed
    You are given P(A|B) and P(A|C) and wish to find P(A|B,C). Let's assume that B,C are independent, and also assume that B,C are conditionally independent given A--that is, P(B,C|A) = P(B|A)P(C|A), and P(B,C) = P(B)P(C).
    So,
    P(A|B,C)=P(A,B,C)/P(B,C) = P(A)P(B,C|A)/P(B,C) = P(B|A)P(C|A) P(A)/(P(B)P(C)) = P(A|B)P(B)/P(A) P(A|C)P(C)/P(A) P(A)/(P(B)P(C)) = P(A|B)P(A|C)/P(A)

    So instead of just multiplying by P(A|C), you multiply by P(A|C)/P(A)
     
    mXSCNT, Apr 14, 2009
  4. Apr 14, 2009 #3

    CRGreathouse

    User Avatar
    Science Advisor
    Homework Helper

    Or, cutting out all the Baysian stuff (good, but if you haven't had a probability class I don't imagine it would make sense):

    If a foo has a 30% chance of getting a degree, but a person (including foos and non-foos) has a 35% of getting a degree, you should be multiplying by .30/.35 rather than .30.
     
    CRGreathouse, Apr 14, 2009
  5. Apr 14, 2009 #4

    Pengwuino

    User Avatar
    Gold Member

    Yah this is what sucks about never having taken a statistics class :(.

    So let me make the problem more accurate and tell me if i do this right. A girl has a 40% chance of having a bachelors degree. Girls who are right handed have a 50% chance of having a degree. Girls who live in california have a 30% chance of having a degree.

    Thus the probability that a girl who is right handed who lives in california will have a (.4*.4*.4)/(.3*.5) chance of having a degree? Thus a 42.6% chance?

    What if say, the 2nd condition "girls who are right handed have a 50% chance of having a degree" was changed to "people who are right handed have a 50% chance of having a degree"?
     
    Pengwuino, Apr 14, 2009
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook