What're The Chances Of This Happening?

[Bill Murphy]

Yeah, prolly belongs on the Prob Forum but I wanted all mah mates here to see it. /images/graemlins/laugh.gif

This guy got a lil' lucky the other day:

http://www.msnbc.com/news/993066.asp

Question: Just how lucky?

Real quick because I'm tired. You quickdraw five numbers btwn 1-52, then a megaball also btwn 1-52. 135,145,920(k) poss. combos.

Guy bought 3 tickets, so assume 15 total 'draws'. He gets two identical draws among the 15, which also turns out to be the winner.

He ALSO has two $150 winning draws, consisting of some combo of 4 hits/ no mega(11,276(j) exact combos) or 3 hits & mega(12,501(h) exact combos).

So what're the odds against this happenning again: something like k^2/15! * h^2/13!, on the high side, subst jj or hj in for the other chances?

Gotta be by far the longest shot to ever come in. Hell, just buying 15 quickdraws and getting a perfect match is pretty long, let alone winnin' the damn thing with 'em /images/graemlins/smirk.gif.

Slightly O/T anyone want to have a guess at the rarest non-gambling event to occur in history? I think there're two contenders:
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The Dionne quintuplets(healthy, naturally conceived) & a family with seven kids, five born on the same day(one set of twins). Read about the latter in Guinness Book, way back when. Them Mcgauhey septuplets don't count. Only one of the kids is perfectly healthy & Mama was on more pills than Rush Limbaugh.

Props, BTW, to the Canadian gov't, for all they did to help the Dionnes have happy, normal lives.

[Easy E]

The odds are too astronomically large to presume anything but that he had numbers chosen on a player's voucher that he played twice, by accident. Notice that he duplicated the $150 win as well.

Either he ran it through twice, or had two copies of the blackout vouchers that they run through the machines.

[George Rice]

You are the second rarest non-gambling event to happen at the time you were born. First, your parents had to meet, with their family trees exactly as they are, going back to the beginning of man. Then the chances of you being born exactly as you were born, assuming they had children, was 2^^23. /images/graemlins/wink.gif

The rarest non-gambling event to happen at the time you were born was the chance that every atomic and sub-atomic particle, as well as anything else in the universe would be in precisely the location in space that it was. The chances of that happening were as close to zero as you can get without actually being zero. Actually, considering the universes' infinite size, there's no chance that happened. Damn, there I go disproving our existence again. /images/graemlins/wink.gif /images/graemlins/wink.gif

Of course my point is that most, if not all, unique occurences are highly improbable. Some to almost an infinite degree. And of course, no two things are exactly the same. /images/graemlins/wink.gif /images/graemlins/wink.gif /images/graemlins/wink.gif

[Wake up CALL]

"And of course, no two things are exactly the same."

For some reason this quote of yours reminds me of Lester Flatt and Earl Scruggs. A fan once listened to Earl play a riff and then asked Earl to "play that one again". Earl quipped "Well, I can play another one that sounds mighty similar but that ones gone. I can never play it again!"

[BruceZ]

135,145,920(k) poss. combos....He ALSO has two $150 winning draws, consisting of some combo of 4 hits/ no mega(11,276(j) exact combos) or 3 hits & mega(12,501(h) exact combos).

These are correct. We should also include getting 5 correct, but it doesn't matter much since these are so much smaller:

Let g = 5 + no mega

g = C(52,5)*52/51 = 2649920

Let f = 4 + mega

f = C(52,5)*52/(5*47) = 575089

Chance of f,g,h, or j = 1 / (1/f + 1/g + 1/h + 1/j) = 1 in 5855.

So what're the odds against this happenning again: something like k^2/15! * h^2/13!, on the high side, subst jj or hj in for the other chances?

Divide by C(15,2) and C(13,2), not 15! and 13! Those are the number of ways to get the 2 winners of each type.

k^2/C(15,2)*5855^2/C(13,2) = 1 in 7.65 x 10^19. That is slightly low since we are approximating the slight chance of getting even more winners. That is, for the binomial distribution, we really would have to add terms for 5,6,7... winners, but the above is a good approximation for this "tail probability". The exact number is less than 7.66 x 10^19.

So that's rarer than 1 in 76500000000000000000 or 76.5 MILLION TRILLION.

[Alobar]

The truly most astronomical occurance would be the situation where there were no astronomical occurances.

[BruceZ]

Post deleted by Mat Sklansky

[Ray Zee]

all kinds of long shots happen as you look back and see something unusual. but it always was something that wasnt expected. so the longshot odds do not apply.
when it is a particular event people are trying to hit, then if it is too long odds, you have to start thinking that it wasnt random at all. either some mistake or cheating. whether this event has those features you guess.

[baggins]

[ QUOTE ]
"And of course, no two things are exactly the same."

For some reason this quote of yours reminds me of Lester Flatt and Earl Scruggs. A fan once listened to Earl play a riff and then asked Earl to "play that one again". Earl quipped "Well, I can play another one that sounds mighty similar but that ones gone. I can never play it again!"



[/ QUOTE ]

great quote!