Probability of an Election Tie

[jimmythegent]

[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!

 

[Office_Shredder]

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

 

[jimmythegent]

Oh, right! Good call... Thanks! :-)