Results 1 to 4 of 4

Math Help - the jury, probability and coins

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    36

    the jury, probability and coins

    A three-man jury (using majority rules) has two members each of whom independently has probability p of making the correct decision and a third member who flips a fair coin for each decision.
    A one-man jury has probability p of making the correct decision.
    Which jury has the better probability of making the correct decision?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by b0mb3rz View Post
    A three-man jury (using majority rules) has two members each of whom independently has probability p of making the correct decision and a third member who flips a fair coin for each decision.
    A one-man jury has probability p of making the correct decision.
    Which jury has the better probability of making the correct decision?
    Draw the contingency tree for the possible outcomes of the three person jury, calculate the leaf probabilities and add up those probabilities corresponding to a correct verdict. Is this greater than equal or less than p.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,707
    Thanks
    1470
    Taking "C" for a 'correct' decision and "F" for a 'false' decision, in order to decide correctly, the decisions of each person must be CCF or CFC or FCC where the first two are the people who decide correctly with probability p and the third is the person who flips a coin. Calculate the probability of each of those and add. Is that greater than p? I think you will find that the answer depends on the value of p.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,663
    Thanks
    1616
    Awards
    1
    Quote Originally Posted by HallsofIvy View Post
    Taking "C" for a 'correct' decision and "F" for a 'false' decision, in order to decide correctly, the decisions of each person must be CCF or CFC or FCC where the first two are the people who decide correctly with probability p and the third is the person who flips a coin. Calculate the probability of each of those and add. Is that greater than p? I think you will find that the answer depends on the value of p.
    What about the case CCC?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Coins Probability
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 9th 2010, 01:05 AM
  2. Coins Probability
    Posted in the Statistics Forum
    Replies: 4
    Last Post: February 10th 2010, 08:07 PM
  3. Probability with a die and with coins.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 14th 2009, 05:55 PM
  4. Replies: 1
    Last Post: October 8th 2009, 10:53 PM
  5. Probability - Coins
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 16th 2007, 11:57 AM

Search Tags


/mathhelpforum @mathhelpforum