[quote author="Daedalus" date=1251211558][quote author="tmare" date=1251202051]I had a math professor years ago at UCI who said that your chances of winning the big pot in the lottery were essentially the same for buying a ticket versus walking down the street and having the winning ticket fall out of the sky and land in your hands. I've never bought a ticket but I think that the dreams that come from a few dollars spent buying a ticket are actually worth it for most people. I guess I can dream of the winning ticket falling from the sky just as well.</blockquote>I think your professor was just trying to make a point about poor odds, assuming a ticket is bought at all. Logically, a random lottery ticket falling from the sky (before the drawing) will have just as much chance of winning as any other lottery ticket, airborne or not. As there are perhaps a million times (total WAG here) more lottery tickets obtained via purchasing than by falling from the sky, the odds of a winning ticket falling out of the sky are minscule--even next to the tiny odds of buying the one winning ticket.
BTW: odds of any one random ticket having the winning numbers is roughly 1 in 25 billion = 1/((56)^5 * 46)
(Odds of winning ticket falling from the sky: ~ 1 in 25 quadrillion.)
If the lottery gets around $100M or higher, and if I happen to be near a liquor store, I'll pony up for some tickets. I've played maybe 5 times in my life. That said, if I don't post after Tuesday it's because I'm probably either in a hospital somewhere, or off busy buying my own Snap On Tool franchise, a large garage, and a bunch of old cars in need of some TLC.
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Odds change once you pull a number out of the pool of entries.
At the beginning, you have 56 possibilities and they pull five numbers,
so odds are (1/56)(1/55)(1/54)(1/53)(1/52) = 1 out of 458,377,920 chances.
But these can be pulled in any order, so you have more than one chance. With five numbers, you have 5! (five factorial) chances,
so odds increase to (5)(4)(3)(2)(1) = 120 out of 458,377,920 chances, or 1 out of 3,819,816 chances.
But the last number, the "Mega Ball", must be pulled last and is part of a separate pool of 46 numbers. Had to look that up.
Will need to multiply the above odds by (1/46).
So your odds of winning, by my calculations, are <span style="color: blue;"><strong>1 in 175,711,536</strong></span>
<em><span style="font-size: 11px;">Happily, I googled "1 in 175,711,536" and was brought to the Mega Millions Odds page for confirmation. Always check your work.</span></em>
If I win, I will spend the rest of my life trying to unlearn this stuff.
Good luck,
IR2
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