[Mega Millions Jackpot] Quick Probability Question

[Warwithin]

Hello everyone,

So, as I'm sure most of you know, the Mega Millions Jackpot is somewhere north of $600 Million for the drawing tonight. This is causing quite the buzz in the U.S. these days.

I just saw a picture on Facebook of a Lottery Ticket held by some radio station. The caption read "If this ticket wins, I'll give $150,000,000 to one person who likes/shares this photo".

Now, over 17,000 people have liked/shared the photo. Given that your odds of being selected are 1:17,000 and the odds of you winning the lottery are something like 1:178,000,000, what does that bring your overall odds of having that ticket win the lottery and you being the one picked for the $150,000,000 prize?

I'm not good with math, so I'm asking for some help here. (inb4 "A very small number". I'm not going to waste my time doing it, but I'm just curious as to what the probability is of someone actually winning that.)

[cvasylum]

If your odds are indeed correct, (1/178,000,000)*(1/17,000) = 3.30469266 × 10-13, or .000000000000330469266. Those are you're odds.

[v2prwsmb45yhuq3wj23vpjk]

If you want to go with a "1 in" type number, it would be 1 in 3,026,000,000,000

[Clockwork Pinkie]

A chance is a chance, no matter how big or small the number is, it's not impossible to win, it's just very very likely to lose.

[Symphonic]

Just waiting for someone to buy 178,000,000 tickets. You'll for sure double your money at least.

[DeltrusDisc]

I don't want to make another topic on the same thing so I'll just add my opinion...

This is getting annoying as can be. The amount of my friends who are posting images of their tickets lately is so damned annoying I almost want to delete them off facebook for wasting their money in such a silly manner. Do they feel like they're making history by getting involved in this? I don't even know what to think. Yes it's a lot of money but it's just such horrible odds...

[belfpala]

I don't want to make another topic on the same thing so I'll just add my opinion...

Annoys me too. You're set for life even at the minimum jackpot. No reason to get excited about it now.

Wait... MEGA DAMAGE. Ok, I understand now.

[vincheto]

If someone spent 178,000,000 on tickets to make sure they won, there is no way of knowing that they will be the only winner. They could end up losing money in the end if 3 or more people win the jackpot. And before you say the odds of that happening are way to slim, it already has. 4 people split a $330 million jackpot and 3 people split a $227 million ticket. With over $1.6 Billion is sales, the odds are that the jackpot will be won by more then 1 person.

[anywherenotes]

Just waiting for someone to buy 178,000,000 tickets. You'll for sure double your money at least.

No, you won't.
If two tickets win the prize, they will share the prize, they won't both get north of 640 mil, but rather 320 mil each.
Or if 3 tickets win, now it's around 200 mil, before cash option and taxes, which will be less than 178 mil.
To my knowledge there have been at least one case of someone buying out the lottery (not megamillions), but 170 mil is a lot of tickets to coordinate, and there better not be more than 2 winning tickets, or you will lose big.

Here are some news stories about buying out the lottery:
http://www.nytimes.com/1992/02/25/us...n-lottery.html
http://www.nytimes.com/1992/03/07/us...-virginia.html

[Gingerhunter247]

You either win or you don't, therefore 1/2.
/trollsnicker

[nyc81991]

I think it's amazing that we have a lottery jackpot of 600 million when we are in such a bad economic crisis. That money could be used for something actually useful.

[DeltrusDisc]

I think it's amazing that we have a lottery jackpot of 600 million when we are in such a bad economic crisis. That money could be used for something actually useful.

Yeah this has always bugged me - granted this is nothing compared to the several trillion buckaroos we have in debt, it is still a hefty chunk. Hell if it all went to charity or getting food, clothes, and shelter for the poor, can you imagine how great that would be for the country?

[Alcsaar]

You guys are getting mad that a lottery exists? Its a business, just like any bussiness. The lottery isn't the only business with 640 million dollars lying around that "could be spent elsewhere"

[semaphore]

Yeah this has always bugged me - granted this is nothing compared to the several trillion buckaroos we have in debt, it is still a hefty chunk. Hell if it all went to charity or getting food, clothes, and shelter for the poor, can you imagine how great that would be for the country?

I think it's amazing that we have a lottery jackpot of 600 million when we are in such a bad economic crisis. That money could be used for something actually useful.

It wouldn't make any difference. Nitpicking over legitimate businesses like this is just a way for people to avoid actually dealing with real issues plaguing the country. It's a distaction, and it's also an excuse to make yourself feel like you are thinking for the greater good when you aren't.

[Clockwork Pinkie]

Yeah this has always bugged me - granted this is nothing compared to the several trillion buckaroos we have in debt, it is still a hefty chunk. Hell if it all went to charity or getting food, clothes, and shelter for the poor, can you imagine how great that would be for the country?

The great thing about the lottery is that way more than 50% of the money they get will be going back into the economy. Giving it to charity or giving homeless people will hurt more than just buying what you want. Win lottery, you buy things, it goes into the economy. Fun fun.

---------- Post added 2012-03-31 at 07:02 AM ----------

I don't want to make another topic on the same thing so I'll just add my opinion...

This is getting annoying as can be. The amount of my friends who are posting images of their tickets lately is so damned annoying I almost want to delete them off facebook for wasting their money in such a silly manner. Do they feel like they're making history by getting involved in this? I don't even know what to think. Yes it's a lot of money but it's just such horrible odds...

Always 50/50 Either you win or you don't.

[volescue]

Just waiting for someone to buy 178,000,000 tickets. You'll for sure double your money at least.

Except you just doubled the ticket pool so there is still a 50/50 chance that you lose, and if we were to say the tickets were even only $1, that is way more money than I would be willing to risk on those odds.

[belfpala]

Always 50/50 Either you win or you don't.

No.

50/50, you get struck by lightning today. Wait, there wasn't a storm where you live...

50/50, you get eaten by a shark today. Oh, yeah, you live about 3-4 hours from an ocean.

[v2prwsmb45yhuq3wj23vpjk]

Except you just doubled the ticket pool so there is still a 50/50 chance that you lose, and if we were to say the tickets were even only $1, that is way more money than I would be willing to risk on those odds.

That's now how it works. There are six numbers drawn. The first five are from a pool of numbers 1 through 56 and the last is from a separate 1-46 pool. In order to actually buy out the MegaMillions lottery, you'd need to buy 175,711,536 lottery tickets. This is because the number of tickets required to cover every set of numbers in the first five plus the last number comes to ((56 * 55 * 54 * 53 * 52) / (5 * 4 * 3 * 2 * 1)) * 46. It goes 56*54 etc. because there are 56 possible numbers for the first draw, 55 for the second (can't get the same number twice), etc. It is then divided by 5*4 etc. because you don't need to match them in a specific order and the ratio of sets of numbers that are the same "match" equals n! whereas n is the number of slots. For example, a 3 digit system with the numbers 1 through 4 has 24 combinations, but only 4 different sets of numbers out of the 24 combinations because each set has 6 different individual combinations. Those sets are 123, 124, 234 and 134. Finally, you multiply by 46 because that's the final number that is pulled from a different pool, and the last number has to match exactly. If the numbers were 1, 2, 3, 4, 5, and 6, you could not win with a ticket that was 6, 5, 4, 3, 2, 1. It would need to be A, B, C, D, E, 6 whereas A-E are the numbers 1-5 in any particular order.

Long story short, buying more tickets doesn't increase any sort of ticket pool, there is a set number of numbers in the pool that doesn't change. This doesn't change the fact that you'd still be competing with everybody else. You still have a 100% chance of winning, you just don't have a 100% chance of winning 100% of the pot.

[Clockwork Pinkie]

No.

50/50, you get struck by lightning today. Wait, there wasn't a storm where you live...

50/50, you get eaten by a shark today. Oh, yeah, you live about 3-4 hours from an ocean.

50/50 chance of a shark being transported to the local aquamarine while you're walking down the street just happens to have a crack in their tank, wossh OHSHI- you're done for. As well as a 50/50 chance of Thor coming down at the same time striking you with lightning. 50/50 no matter what. 1-to-??? odds is just pointless math to see how big of a number they can get for their own personally enjoyment.

[v2prwsmb45yhuq3wj23vpjk]

50/50 chance of a shark being transported to the local aquamarine while you're walking down the street just happens to have a crack in their tank, wossh OHSHI- you're done for. As well as a 50/50 chance of Thor coming down at the same time striking you with lightning. 50/50 no matter what. 1-to-??? odds is just pointless math to see how big of a number they can get for their own personally enjoyment.

Odds are not pointless. Going by your logic, it isn't even 50/50, it's 100/0. It's not 50/50 you win or lose, it's 100/0 you lost or 100/0 you won as soon as you've bought the ticket.

Odds help to mitigate cost when allocating resources for things that have a great deal of chance or unresolved factors involved. Warfare, for example.