# Calculating probability of voting results from small sample aize

2 million people voted in a poll for their favourite song. 35,000 votes have been counted so far, of which:

• 575 votes are for Song A
• 466 votes are for Song B
• 393 votes are for Song C
• (And the remaining votes for various other songs)

What is the % likelihood that Song A will win the poll?

• If you are asking specifically what is the probability of this event happening then you could estimate this using Bayesian statistics and posterior sampling. – user2974951 Jan 8 at 15:03
• It depends very much on how the votes are counted. If they are counted in some systematic way, such as the order in which they are received, then (without making some strong assumptions which you will need to assess separately) you have no basis to suppose that the results of the first 35,000 votes tell you much, if anything at all, about the remaining votes. It won't help if you use Bayesian methods (cc @user2974951) or any other method. – whuber Jan 8 at 15:16