Results 1 to 2 of 2

Math Help - conditioning to provide a general formula

  1. #1
    Member
    Joined
    Aug 2010
    Posts
    77

    conditioning to provide a general formula

    Independent trials that result in a success with probability p and failure 1 - p are performed. Let P_n denote the probability that n Bernoulli trials result in an even number of successes (0 considered even). Show that
    P_n = p(1-P_{n-1}) + (1-p)(P_{n-1})

    I am not sure what events to condition on to provide this formula. I am fairly stumped!
    Last edited by CaptainBlack; April 7th 2011 at 03:00 AM. Reason: correct LaTeX
    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 FGT12 View Post
    Independent trials that result in a success with probability p and failure 1 - p are performed. Let P_n denote the probability that n Bernoulli trials result in an even number of successes (0 considered even). Show that
    P_n = p(1-P_{n-1}) + (1-p)(P_{n-1})

    I am not sure what events to condition on to provide this formula. I am fairly stumped!
    This is a 1-term recurence. The probability of an even number of successes in n trials is the sum of a odd number of successes in the previous n-1 trials and a success in the n-th trial and the probability of an even number of successes in the privious n-1 trials and a failure in the n-th trial.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. General Diagonal Formula
    Posted in the Geometry Forum
    Replies: 9
    Last Post: November 14th 2011, 05:28 PM
  2. General formula of a series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 20th 2010, 08:55 PM
  3. sequence general formula
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 28th 2009, 01:15 PM
  4. General formula of derivative
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 4th 2009, 06:40 AM
  5. General Formula
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 20th 2009, 01:27 PM

Search Tags


/mathhelpforum @mathhelpforum