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Probability of an Election Tie

  1. Dec 6, 2007 #1
    [SOLVED] Probability of an Election Tie

    1. The problem statement, all variables and given/known data

    There is a town of 4000 people. What is a probability of an election with two candidates having a tie if each person has an equal probability of voting for each of the 2 candidates.

    2. Relevant equations


    3. The attempt at a solution

    Okay, so I thought [tex]\binom{4000}{2000}[/tex] * 2 * [tex]\frac{1}{2}^{2000}[/tex] to find all the ways you can choose 2000 people from the 4000. Then you multiply by the probability of these 2000 choosing one candidate. You multiply everything by 2 since those 2000 could vote for the other candidate as well.

    Does this sound like a reasonable answer or is there something I'm missing/doing wrong.

    Any help would be greatly appreciated. Thanks a lot!
    Last edited: Dec 6, 2007
  2. jcsd
  3. Dec 6, 2007 #2


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    You don't need to multiply by 2 for the other candidate vote, as that was considered when you tried picking 2000 people, and picked exactly the other group of 2000 to vote for the first candidate
  4. Dec 6, 2007 #3
    Oh, right! Good call... Thanks! :-)
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