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Probability - Coin Toss - Find Formula

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Suppose a fair coin is tossed n times. Find simple formulae in terms of n and k for

    a) P(k-1 heads |k-1 or k heads)
    b) P(k heads | k-1 or k heads)


    2. Relevant equations
    P(k heads in n fair tosses)=binomial(n,k)/2^n (0<=k<=n)


    3. The attempt at a solution
    I'm stuck on the conditional probability. I've dabbled with it a little bit but I'm confused what k-1 intersect k is. This is for review and not homework. The answer to a) is k/(n+1).
    I tried P(k-1 heads | k heads)=P(k-1 intersect K)/P(K heads)=P(K-1)/P(K). I also was thinking about P(A|A,B)=P(An(AuB))/P(AuB)=P(Au(AnB))/P(AuB)=P(A)/(P(A)+P(B)-P(AB))

    Thanks!
     
  2. jcsd
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