Lottery Math

Factual Questions
1

I blew some money on the Megamillions lottery the other day and was looking at the odds on the back, and the math just isn’t making any sense to me. You pick 5 numbers between 1-75 and one ‘megaball’ between 1-15. You can win your dollar back if you match the megaball and none of the numbers.

So the odds of being even would be 1:15, right? Each megaball has equal odds of being picked.

Yet the Illinois Lottery tells me my odds are 1:21.

Are they just total idiots or have I missed something with my math?

2

The odds that you picked the megaball is indeed 15:1.
But the odds that you a) picked the megaball, and b) matched absolutely none of your other numbers is 21:1.

3

If I understand that chart correctly, 1:21 are the odds of matching the Megaball and getting zero other numbers correct.

4

“Probability” vs “odds” nitpick: The probability of getting the megaball would be 1/15. The odds would be 1 to 14, under the method of reporting odds that I’m familiar with, because there’s 1 “good” ball and 14 “bad” ones.

5

Thanks all!