I am trying to figure out if there is a way to detect suspicious voting behavior in my country in South America. The way elections work is that each region has a several election centers with voting tables, with an average of 229 voters each (+/- 50).
One candidate got 0 votes in 18 voting tables, which I think is highly unlikely, despite the fact she only had 10.7% of the vote in that region overall. So, here are the facts:
Total Region Votes: 722,793
Candidate A: 645,152 ( 89.258%)
Candidate B: 77,641 (10.742%)
Voting Tables: 3159
Votes per table (total votes/voting tables): 229 (+/- 50)
Question, what is the probability that Candidate B got 0 votes in 1, 5, 10 and 18 voting tables?
Put another way, if we were to take 3159 random samples of 229 votes each (+/-50) from all the votes (722,793) what is the probability of pulling out "0" votes on a sample for Candidate B once, 5, 10 and 18 times? I assume the probability would fall exponentially.
If there is a way to simulate this in Excel, any detail would be much appreciated.
p.s. This assumes that the votes per table are normally distributed, which I do not know for a fact, but given the very large sample size and similarities in voter preference composition for that region I suspect would be the case.