Statistics: Winning the Lottery

To my dismay, I didn’t win the $636,000,000 MegaMillions lottery the other night. I guess I won’t be buying a yacht anytime soon…

According to the odds listed on the bottom of the of the ticket, there is a 1 in 258,890,850 change of winning. That number comes from a formula called the Combination Formula, which is:

$C = \frac{!n}{!r(n-r)!}$
Where r is amount of numbers you can pick, and n is total number of choices.
Think “N choices, choose R“

$258,890,850 = (\frac{!75}{!5(75-5)!}) * (\frac{!15}{!1(15-1)!})$
In MegaMillions, you pick 5 regular numbers from the pool of 75 and a MegaBall which is 1 number from a pool of 15.

$\frac{1}{258,890,850}$
258,890,850 is the total number of combinations. If you have a single ticket, your odd of winning are 1 in 258,890,850.

$\frac{2}{258,890,850}=\frac{1}{129,445,425}$
Simply having 2 tickets doubles your odds of winning.

What if you bought 2 tickets for every drawing for your entire life? Then would you have a chance of winning?

$2\ drawings\ per\ week\ *\ 52\ weeks\ per\ year\ =\ 104\ drawings\ per\ year$
MegaMillions draws numbers on every Tuesday and Friday.

$80\ years\ old\ -\ 24\ years\ old\ =\ 56\ years\ to\ play$
Let’s assume I start today. I’m 24 years old and the average life expectancy of a Wisconsinite is 80 years old.

$56\ years\ to\ play\ * \ 104\ drawings\ per\ year\ =\ 5,824\ drawings\ over\ lifetime$
Now we take the years I have left to play multiplied by the drawings per year to get 5,824 drawings over my life.

$\frac{5,824}{258,890,850}=\frac{1}{44,452}$
If I buy 1 ticket for each of the 5,824 drawings, it would cost $5,824 and my odds of winning are 5,824 in 258,890,850. This roughly equals 1 in 44,452. This doesn’t sound like a great ROI.

$\frac{11,648}{258,890,850}=\frac{1}{22,226}$
I can double my odds if I buy 2 tickets for each of the 5,824 drawings. Again, it would cost $11,648 and my odds of winning are 11,648 in 258,890,850. This roughly equals 1 in 22,226. Better, but not sure I’m will drop that kind of dough.

$\frac{58,240}{258,890,850}=\frac{1}{4,445}$
Even if I bought 100 per drawing, the odds are pretty slim.

To put these numbers in prospective,

Odds of having twins: 1 in 726
Odds of a male developing breast cancer: 1 in 1,000.
Odds of being struck by lightning (over a lifetime): 1 in 3,000.
Odds of being eaten by a shark: 1 in 13,729

What if you bought 2 tickets for every drawing for your entire life? Then would you have a chance of winning?

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