1. Limited time only! Sign up for a free 30min personal 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!

Confusion about conditional probability

  1. Oct 28, 2015 #1
    1. The problem statement, all variables and given/known data
    Suppose that 70% of the statisticians are shy, whereas 30% of the economist are shy. Suppose also that 80% of the people at a large gathering are economists and the remaining 20% are statisticians. If you randomly meet a person at the gathering and the person is shy, what is the probability that the person is a statistician?
    How can you interpret this statement?
    Suppose that 70% of the statisticians are shy.

    It sounds to me like the prob that we choose a person who is and statistician and is shy
    but it is the prob that we choose a person who is shy given that he is an statistician


    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Oct 28, 2015 #2

    andrewkirk

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

  4. Oct 28, 2015 #3
    this is my problem

    How can you interpret this statement?
    Suppose that 70% of the statisticians are shy.

    It sounds to me like the prob that we choose a person who is and statistician and is shy
    but it is the prob that we choose a person who is shy given that he is an statistician
     
  5. Oct 28, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You have it backwards. The person you meet is shy---that is, you are given that he/she is shy. So, you want P(stat|shy). Note that you already know the opposite conditional probability P(shy|stat), which was specified as part of the input data for the problem
     
  6. Oct 28, 2015 #5

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    To understand these sort of questions I suggest drawing a probability tree and working backwards from right to left.

    This allows you to see all the cases where there is the specified outcome (here that someone is shy) and allows you to map back to calculate the likely source of the outcome: Of all the shy people how many of them are statisticians.
     
  7. Oct 28, 2015 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I think MathNoob is asking for clarification on one of the stated facts, not yet to the point of addressing the question.
     
  8. Oct 28, 2015 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, that would match "70% of people are shy statisticians".
    The "of" indicates the population to be sampled. 70% of statisticians have property P means that if we sample all the statisticians then 70% of them will have the property, so if we pick one at random then there is a 0.7 probability she will have that property.
     
  9. Oct 28, 2015 #8

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Here's how I would do this: Imagine 100 people at the gathering. 80% of them, 80, are economists and 20%, 20, are statisticians. 70% of the statisticians, .70(20)= 14, are shy and 30% of the economists, .3(80)= 24, are shy. So there are a total of 14+ 24= 38 shy people, and 14 of them are statisticians. "Given that the person is shy" means that we restrict ourselves to only shy people and determine what percentage of them are statisticians.

    Relevant equations


    3. The attempt at a solution[/QUOTE]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Confusion about conditional probability
Loading...