Carl Bialik has written about lottery coincidences in his WSJ print column and on The Numbers Guy blog, inspired of course by the recent consecutive draws in the Bulgarian lottery. Addressing my recent confusion, he sheds a little light on why likelihood estimates varied so much:
The probability of Bulgaria's repeated winning numbers became a subject of some disagreement. A Bulgarian mathematician estimated the probability at 1 in 4.2 million, a figure that was widely reported. Clio Cresswell, a mathematician at the University of Sydney in Australia, came up with 1 in 14 million. Many others arrived at 1 in 5.2 million.
One explanation for the wide range is that Bulgaria has multiple lotteries. Dr. Cresswell's calculations relied on a different Bulgarian lottery with numbers ranging from 1 to 49. Mr. Smith and others made their calculations assuming the possible numbers went up to 42, the correct range for this particular lottery. As for the 1-in-4.2 million estimate, the Bulgarian mathematician didn't respond to requests for comment.
The blog post in particular is full of really interesting links - I especially enjoyed Professor Leonard Stefanski's account (pdf) of trying to reconcile accurate statistics with the media's desire for sensationalism.