Using Simple Statistics to Catch MIT FBI Murderers updated

(updated for 22 death threats)

The murderers sent Dr. Egan 22 coded death threats via emails and letters after they killed Leah Egan.
The FBI counterintelligence agents that are part of their crime ring like to document their crimes and mock their victims in coded messages.
Their best defense against the charge of sending death threats is to simply say, “We did not send any death threats. The patterns in the letters and emails are random and happened by chance.”
How do we prove these messages are not random, but instead were purposefully coded to be death threats?
There is an old saying: “Once is coincidence, twice is suspicious, and three times is enemy action.”
We can easily calculate the probability that a set of unusual events one after the other is real or random.
The area of statistics used here is referred to by various names: the coin toss test, the probability version of Pascal’s Triangle, or the Binomial Theorem.
Anyone can do the calculations with a cheap calculator or Excel or Google sheets.