In 1985, Evelyn Marie Adams won $3.9 million in the New Jersey lottery. Four months later, in 1986, she won again; it was $1.4 million this time! The New York Times ran an article claiming that the probability of such an event was one in 17 trillion. Their argument must have been:
The probability of winning the first lottery – 6 numbers out of 39:
1/39C6 = 1/3262623
The probability of winning the first lottery – 6 numbers out of 42:
1/42C6 = 1/5245786
The chance of her winning both = (1/3262623)x(1/5245786) = 1/17 x 1012
This was actually the correct answer to a wrong question. The question should have been:
“What is the probability that both tickets will be winners if you buy precisely two tickets for the New Jersey state lottery?”
Instead, the probability here was:
What is the chance that someone, out of millions of people buying lottery tickets each week in the United States, hits the lottery twice in four months?
Stephen Samuels and George McCabe of the Department of Statistics at Purdue University, who wrote in the newspaper’s opinion column, estimated that to be 1 in 30.
Reference
More Lottery Repeaters Are on the Way: NYT
