## September 9, 2006

### The odds were 1 in 3,669,120,000,000.

Woman wins \$1 million in a scratch card lottery, after previously winning \$1 million on another scratch card. She works in a deli making sandwiches, and even after this new win, she's going to keep making the sandwiches. Will she keep buying scratch cards?

The Drill SGT said...

I think those odds are overstated.

I would think that odds shown of:

Lottery officials say that in 2002 Ms Wilson beat odds of 1 in 5.2 million when she won the Cool Million scratch card game

and

Then last month she beat odds of 1 in 705,600 by winning New York lottery's Jubilee scratch card game.

mean that those are the odds given 1 draw of a win in each of the contests.

so the odds given of 3.6x10**12 are the odds 4 years ago of winning one draw of the first lottery and then today winning another single draw of the second lottery.

that is a 2 event joint probability

given that she bet more than once on the first and second lottery he odds went down a lot and of course,

once she had won the first lottery, then the odds of winning the second (depending on how many times she bought a ticket) were much less than 1 in 705,000

but it sounds good

Beau said...

How could you not?

Amazing odds...how much is three and a 12 zeros anyway. Three cajillion?

jimbino said...

The odds that an arbitrary .
person who was foolish enough to participate in both lotteries would win both might well be the stated 1 in 3 trillion, but the odds that the winner in the first lottery would win the second were merely the 1 in 800,000 or so that it took to win the second lottery.

The odds that someone who won some earlier lottery wins some second lottery is even more favorable than 1 in 800,000.

Folks in general, and math-challenged lawyers and judges, in particular, are notoriously incapable of handling simple probability.

Y'all need a refresher course in Paulos' book Innumeracy.

dearieme said...

The question is whether one can jog along on a couple of million.

john(lesser) said...

Also relevent, odds are based on a one time opportunity. Ever walked up to the counter in a bodega/deli/quick-e-mart, only to find the cashier scratching off a row of these things ?

JohnF said...

drill sgt has it almost right. If the odds given on each lottery are correct (1 in 5.6 million and 1 in 705,600), then, before any tickets are bought, and assuming she will buy one of each, the odds of winning both are indeed 3.6 (actually, 3.7) in 10 trillion.

However, after the first lottery, her chances of winning the second are the same as everyone else's, i.e., 1 in 705,600. The fact that she won the first lottery is no more relevant than the fact that, say, lightning hit a tree outside her house prior to the second lottery.

Anonymous said...

No balogna-- two million-dollar tickets in just fours years? That's a lot of bread, for pita's sake. And we know it ain't chopped liver, because she's bringing home the bacon! But just think of all the turkey tix she bought over the years,and, wurst, the pickle she'll be in when distant cousins from Dijon pick a beef with her over her not spreading the lettuce around enough. She'll have to change the lox, I imagine, and get the head cheese of an accounting firm to help her go Swiss quickly before she makes a hash of it.

(I mustard the best effort I could, guys, and for your sakes left off red herring and Mayo Clinic.)

RHodnett said...

Do you realize how many scratch cards she'll be able to buy with a million dollars?

JohnF said...

When I said 3.7 in 10 trillion, I should have said 1 in 3.7 trillion, as in the title of Ann's post. Sorry for the error.

Dave said...
This comment has been removed by a blog administrator.
Dave said...

OK, quick math lesson here: the odds of having won the second lottery are no more affected by having one the first lottery than the odds of scoring a second hole in one in a round of gold are affected by having scored the first hole in one.

In other words, these are independent events, the odds of each of which are unaffected by the other.

JohnF and Drill Sgt have it right here.

Dave said...

"having one the first lottery"

Should be "having WON the first lottery."

So, I'm numerate but illiterate I guess.

Damned homonyms!

Dave said...

And this should be corrected to: "the odds of scoring a second hole in one in a round of gold"

That would be a round of GOLF.

Not a good start for me with the typos.

Ann Althouse said...

On the math point, I think clearly the perspective taken is before she's bought any tickets, but the key missing consideration is that she didn't just buy two tickets. She's probably bought hundreds or thousands of tickets.

Plus she's lucky!

Cat said...

Jim - that foolish person now has \$2mm more than you.

Kill joy!