Probability of an Election Tie

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SUMMARY

The probability of an election tie in a town of 4000 people voting for two candidates can be calculated using the binomial coefficient. The correct formula is \(\binom{4000}{2000} \cdot \left(\frac{1}{2}\right)^{4000}\), which accounts for all possible combinations of 2000 votes for each candidate. The initial confusion about multiplying by 2 for the second candidate was clarified, as the selection of 2000 inherently includes both candidates' votes.

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  • Understanding of binomial coefficients, specifically \(\binom{n}{k}\)
  • Basic probability concepts, particularly with equal likelihoods
  • Familiarity with combinatorial mathematics
  • Knowledge of election voting systems and their statistical implications
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[SOLVED] Probability of an Election Tie

Homework Statement



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.

Homework Equations



:-)

The Attempt at a Solution




Okay, so I thought \binom{4000}{2000} * 2 * \frac{1}{2}^{2000} 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:
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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
 
Oh, right! Good call... Thanks! :-)
 

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