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!

Conditional Probability Coin Flipping Question

  1. Dec 7, 2013 #1
    1. The problem statement, all variables and given/known data
    The following experiment involves a single coin with probability p of heads on any one flip, where
    0 < p < 1.

    Step 1: Flip the coin. Let X = 1 if heads, 0 otherwise.
    Step 2: Flip the coin (X + 1) times. Let Y = the number of heads obtained in this step.
    Step 3: Flip the coin (X + Y + 1) times. Let Z = the number of heads obtained in this step.
    Let T denote the total number of heads across all three steps.

    What is P(X = 1|Z = 0)?


    2. Relevant equations
    [itex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/itex]



    3. The attempt at a solution
    I think I have been thinking about this too long and am just confusing myself. My first gut reaction was to say that no matter what the outcome of Z, since the coin isn't changing, the probability of it coming up heads on any given flip (ie P(X = 1)) will be p.
    But since you are flipping a variable number of times to get Z, it seems your chance of getting Z = 0 would be greater with a smaller number of flips, which would be more likely if you begin with X=0 than X=1. Does this even matter?
    I tried using the above conditional probability formula as well, but it got ugly quickly in trying to calculate the numerator. Is there a less thorny method that I'm missing?
     
  2. jcsd
  3. Dec 7, 2013 #2

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Have you throught about doing a tree of the possibilities?
     
  4. Dec 7, 2013 #3
    I did try one, but I was having trouble keeping track of all the relevant numbers: possible flips, number of heads, corresponding probabilities that I was hoping there might be a clearer way. I might have to give it another crack...
     
  5. Dec 7, 2013 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You MUST keep track of the possible numbers of heads, etc., whether it is troublesome or not. And yes, it might be lengthy and require quite a bit of work, but that is the most straightforward way to solve the problem.
     
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: Conditional Probability Coin Flipping Question
  1. Coin flip Probability (Replies: 1)

Loading...