CNY Mathletics: Majority Rules

Consider an election with two candidates: A and B. The winner is the candidate with the most votes. Say A receives α votes and B receives β votes. Candidate A wins the election. Now, during the process of counting the votes, a running total is kept for each of the candidates. What is, in terms of α and β, the probability that the running total for candidate A remains greater than of equal to the running total of candidate B throughout the entire vote counting process?

#Combinatorics #Probability

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

What is CNY Matheletics?

To me, CNY stands for Chinese New Year, and I am in the midst of planning what to do for that lol.

Calvin Lin Staff - 6 years, 5 months ago

It's just a very casual and fun mathematics competition. CNY stands for central New York, aka the non-exciting part of the state. Realizing now that I should've specified! CNY Mathletics has some pretty cool problems now and then, but overall, it's not very challenging.

Ryan Tamburrino - 6 years, 5 months ago

I posted a note regarding this here. See @Finn Hulse 's solution.

Pranjal Jain - 6 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$