Results 1 to 2 of 2

Math Help - Monty Hall Problem

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    15

    Monty Hall Problem

    The original problem is that there are three doors (2 with goats and 1 with a car behind it). A person chooses one of the three doors then the host picks another with a goat behind it. The person can then choose to pick the other unopened door or stick with his initial choice.

    I am given an extension of this problem and I need help with it.
    So the question is there are N doors, C cars, D doors that are opened, and G goats where G = N-C

    Now I need to find

    the probability that the person wins the car given he switches and
    the probability that he wins the car given he does not switch

    I am not quite sure how to do this. I think Bayes theorem is needed, but I don't know what to do.
    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 helpwithassgn View Post
    The original problem is that there are three doors (2 with goats and 1 with a car behind it). A person chooses one of the three doors then the host picks another with a goat behind it. The person can then choose to pick the other unopened door or stick with his initial choice.

    I am given an extension of this problem and I need help with it.
    So the question is there are N doors, C cars, D doors that are opened, and G goats where G = N-C

    Now I need to find

    the probability that the person wins the car given he switches and
    the probability that he wins the car given he does not switch

    I am not quite sure how to do this. I think Bayes theorem is needed, but I don't know what to do.
    The second part is trivial, it is the same as the probability of winning if no doors were opened.

    The first part I would draw a contigency tree for with two main branches, the player switches when there is a car behind their door, and the player switches when there is no car behind their door. We already know the probabilities for these two branches and the winning probability is now the chance that a door is picked with a car from the remaining doors and cars.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Monty Hall problem with 4 doors
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 9th 2011, 05:24 PM
  2. Monty Hall goes Car-Goat-Key
    Posted in the Math Puzzles Forum
    Replies: 4
    Last Post: October 4th 2009, 06:09 PM
  3. The Monty Hall Paradox
    Posted in the Math Challenge Problems Forum
    Replies: 3
    Last Post: December 27th 2007, 06:26 PM
  4. Monty Hall Variation
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 6th 2007, 09:14 PM
  5. Monty Hall Problem
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: April 23rd 2006, 06:00 AM

Search Tags


/mathhelpforum @mathhelpforum