Here is my ticket for the May 18 Power Ball lottery. Here are the winning numbers: 10 12 14 22 52 and the Power Ball was 11. You can see I didn't pick one number correctly.
Being the geek that I am, I immediately wondered what the probability was that someone could pick six numbers and not get one right.
Calculating the probability is simple. The probability is just the number of desired outcomes divided by the total number of outcomes. Now it gets a bit more complicated if you haven't had a statistics course.
In the Power Ball lottery, there are white balls numbered 1 through 59 and red ones (the Power Balls) numbered 1 through 35. We need to know how many possible drawings there are. In the vernacular of statistics and probability, we want the number of possible combinations.*
Let's first calculate the number of ways there are to pick 5 numbers out of 59.
The ! means factorial; that is 5! is 1 X 2 X 3 X 4 X 5. The answer is 5,006,386.There are only 35 ways to pick one number out of thirty-five. So the total number of combinations is 5,006,386 X 35 = 175,223,510. Because there is only one winning combination, the probability of winning is 1/175,223,510.
In order to pick not even one number correctly, we need to exclude the 5 correct white balls and then calculate the number of ways to pick five numbers out from 54 white balls.
This equals 3,162,510. Then multiplying by 34, the number of non-winning red balls, yields the number of combinations with no correct numbers. 107,525,340.
Now we're ready. The probability of picking six numbers in the Power Ball lottery and not having a single one correct is
Pretty damn likely, isn't it.
Let's go back and examine the likelihood of winning. One chance out of 175.2 million. Suppose every adult in the US bought a Power Ball ticket. That's 192.9 million people. This means that if every adult played, there's about a 90% chance that someone will win. The actual probability that someone will win is much less, since only 32 states plus the District of Columbia and the U.S, Virgin Islands participate.
Unfortunately, the numbers don't lie. That winner will never be me or you.
Not winning may be the best thing to ever happen to us though. The National Endowment for Financial Education estimates that 70% of those who enjoyed quick wealth lose that money within several years.
It's not even a good deal for the states. The lottery turns out to be a regressive tax, a tax that hits the poor the hardest. In most, if not all, lottery proceeds are meant to be spent on education. Yet in California, lottery revenues in 2010 added only 1.3% to the education budget.
So I only play when the jackpot hits enormous numbers and then I buy one ticket. You know the difference between buying one Power Ball ticket and buying ten? You're out $18 more when you buy ten.
* If the order in which the balls are picked made a difference, we would need to calculate the number of permutations. In the May 18th Power Ball for example, it didn't matter that the 22 ball was picked before the 10 ball.