Results 1 to 1 of 1

Thread: Net effect of more draws with lower "accuracy"...?

  1. #1
    Jul 2010

    Question Net effect of more draws with lower "accuracy"...?

    Dear all,
    I am struggling with the following problem:

    We take n + 1 independent draws (n even), where each draw has a “success probability” gamma > 1/2. Let S be the probability of a majority (i.e. more than 50%) “successes.”

    What happens to S if we increase the number of draws by 2 (to keep n even) but , at the same time, decrease gamma in such a way that probability of a tie one draw before the end -- i.e., after n draws, resp., after n+2 draws -- remains constant?

    Numerical calculation show quite convincingly that S falls. But I cannot prove it!

    I have written out the problem in the attachment. Here, Prob(Pivot) denotes the probability of a tie after n draws (respectively, n+2 draws). Such a tie one draw before the end means that all draws are "pivotal," i.e., decisive.

    Very much looking forward to any suggestions that people may have.


    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Oct 17th 2011, 02:50 PM
  2. Replies: 2
    Last Post: Jun 4th 2011, 12:11 PM
  3. Replies: 2
    Last Post: Apr 24th 2011, 07:01 AM
  4. Replies: 1
    Last Post: Oct 25th 2010, 04:45 AM
  5. Replies: 1
    Last Post: Jun 4th 2010, 10:26 PM

Search Tags

/mathhelpforum @mathhelpforum