Results 1 to 2 of 2

Math Help - Coin game probability - simple set up, tricky to calculate

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    21

    Coin game probability - simple set up, tricky to calculate

    Suppose Bob flips a coin N times, and Jeff flips a coin N+1 times (N is an arbitrary positive integer). What are the odds that Jeff gets strictly more heads than Bob?

    I'm stuck here.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2011
    Posts
    21
    Actually, I think I may have found a solution, but would love for someone to verify.

    Assume Bob and Jeff both flip the coin N times. Either Bob gets more heads (Event B), Jeff gets more heads(Event J), or they tie (Event T). Obviously P(B) = P(J), and P(B) + P(J) + P(T) = 1. We can also see that P(J) + (1/2)*P(T) = 1/2 with just a little algebra.

    Now, if Jeff flips one more coin after this (making a total of N+1 flips for Jeff), what is the probability he has strictly more heads than Bob after this extra flip? If he was already behind Bob, then he can't have strictly more heads than Bob now no matter what the outcome of the extra flip. If he was already ahead of Bob, then he'll have strictly more heads no matter what the outcome of the extra flip. And if they were tied, then there's a 1/2 chance that he will now have strictly more heads than Bob and a 1/2 chance he won't.

    So via the statement P(J) + (1/2)*P(T) =1/2, we can say that the probability Jeff gets more heads in N+1 throws than Bob gets in N throws is 1/2.

    Does this look sound?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: January 9th 2012, 12:48 PM
  2. Replies: 5
    Last Post: January 4th 2012, 02:49 AM
  3. Coin Game
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2011, 12:53 PM
  4. Algorithm Need To Calculate Memory Game Score
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: February 7th 2011, 12:02 PM
  5. tricky biased coin flipping question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2010, 07:05 AM

Search Tags


/mathhelpforum @mathhelpforum