Big Money, Tiny Chances
How likely are you to win the lottery? When the US Mega Millions lottery reached a total jackpot of $1.6bn, this is the key question for potential players.
As part of the Statistical Ambassador programme for the Royal Statistical Society, I was asked to give context to this probability for BBC News.
One in 302m: The probability of winning the Mega Millions lottery with a single ticket was one in 302,575,350.
That is extremely unlikely: Winning that lottery is more unlikely than tossing 28 consecutive Heads on a fair coin, or rolling 10 consecutive sixes on a fair die, or being killed by lightning.
Calculating the Odds
Since October 2017, the US Mega Millions lottery requires players to select five out of 70 white balls, and one Mega Ball (from 25 possibilities).
We do not care about the order, so the probability of matching the first ball is 5/70. Given we have matched the first ball, the probability for the second ball is 4/69. Following this method, and multiplying by 1/25 for the Mega Ball, we get the probability of winning the jackpot with a single ticket is one in 302,575,350. This is usually rounded to one in 300m.
For the UK National Lottery, players must match six numbers — from 59 balls — to win the jackpot. The jackpot probability is one in 45,057,474.
What is more likely?
To give context, we can compare the US Mega Millions jackpot probability to other common probability games.
Flipping a fair coin has a equal chance of 50% for Heads and Tails. Flipping 28 consecutive Heads has a probability of one in 268m.
Dice are also common. Rolling 10 consecutive sixes happens one in every 60m times, using a fair die.
Imagine someone tells you the first three digits of their mobile phone number (e.g. ‘078’). The chance you would correctly dial their full number randomly first time is one in 100m.
The two mortality likelihood estimates are lifetime figures.
It is based on US mortality data from 2015, dividing the number of deaths in that year by the population. For life estimates, multiply that figure by average life expectancy. The calculation was made by the US National Safety Council. It is usually called the ‘crude’ mortality rate, since no adjustment for age is made.
In hindsight, it would have been preferable to give annual mortality rates:
- Dying in a plane crash in the next year (one in 16m);
- Dying by a lightning strike in the next year (one in 9m).
It is important to give context to figures in news reports, and for statisticians to be forthright about statistics in public discussions.