The Mega Millions jackpot keeps growing and growing, now up to $1.6 billion after Friday night’s $1 billion drawing produced no winners.
It turns out that given the number of tickets sold, that wasn’t an overly surprising result.
In a Mega Millions drawing, five numbered balls are drawn from a drum with 70 balls, and a final bonus ball is drawn from a drum with 25 balls. To win the jackpot, your ticket must exactly match the numbers drawn.
There are 12,103,014 possible combinations of the first five numbers ranging from 1 to 70. Multiply that by the 25 options for the final ball and you get a total of 302,575,350 possible Mega Millions draws. That means any given ticket has a 1-in-302,575,350 chance of winning, or about a 0.00000033% probability.
Another way of looking at that is that a single ticket has a 99.99999967% chance of losing the jackpot. That extremely high chance is one of the main reasons it probably isn’t a good financial decision to play Mega Millions.
But this is looking at just one ticket. What happens when we consider the millions of people who bought lottery tickets before Friday night’s drawing?
As long as we make the reasonable assumption that people are generally picking their Mega Millions numbers randomly and in such a way that one person’s picks have no influence over anyone else’s, it’s fairly straightforward to estimate the overall probability that no one won the jackpot based on the number of tickets sold.
The assumption that people aren’t influencing one another’s picks is called statistical independence. The handy thing about independent events is that if we want to know the probability that a whole bunch of independent events all happen together — like, say, the probability that several million people all lost the Mega Millions jackpot — all we have to do is multiply the individual probabilities of each of those events.
According to LottoReport.com, a website that uses lottery sales figures to estimate the number of tickets sold for any given drawing, 280,217,678 Mega Millions tickets were sold before Friday’s drawing. So we can find the probability that all those tickets were duds by multiplying together the probability that any one ticket is a dud — as we saw above, about 99.99999967% — 280,217,678 times. That is, we take 99.99999967% raised to the 280,217,678th power.
While that would be daunting to try to do by hand, it’s trivial for a computer. Indeed, we can estimate quite easily the probability that no one wins a Mega Millions jackpot for just about any number of millions of tickets sold.
Based on all this, there was about a 39.6% chance of Friday night’s outcome of no one winning the jackpot: