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[Mathematics] Weird Lottery Probability - Printable Version

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[Mathematics] Weird Lottery Probability - Eclipse - 03-30-2015

The probability of winning the lottery. Why is it that we know the probability is so low, and yet we still pursue with the vain hope that we'll win? In this thread, I'll go over the strange and infinitesimal probability of actually winning.

In normal lottery, you have 49 numbers, and you get to pick any 6 from them. So, you can easily say that the probability of one of your options being correct is 1/49. Each option can only be selected once, so the probability that the next option is correct is 1/48, and so on. This can be represented mathematically:

Code:
1 / (49*48*47*46*45*44)
= 1/10,068,347,520

Or 1 in over 10 Billion... That's insane, but not actually correct. We haven't countered in the fact that the order of the selected numbers isn't important. So if I pick 1, 2, 3, 4, 5 and 6, and the winners are 6, 5, 4, 3, 2 and 1, I still win. There are 6 winners, so we do 6!, or 1*2*3*4*5*6. This equals 720. Now we get the answer above, and divide by 720:

Code:
10068347520/720
= 13,983,816

The probability of winning the lottery, is 1/13983816, which is nothing to sniff at. It's fucking tiny. Let's put this into perspective:

1 in almost 14 million... In decimal, that's 0.0000000715112384. The sum of the total road deaths and serious injuries caused by road accidents in the UK in 2014 was 24,580. There are 64,100,000 people in the UK, so as a UK resident, the chances of you being involved in one of these accidents in a year is:

Code:
24580/64100000
= 0.0003834633385335

That's a much greater chance than the lottery. Let's divide by 12 to get a month:

Code:
0.0003834633385335/12
= 0.000031955278211125

Still not enough. The chance in the next week:

Code:
0.000031955278211125/4.34812
= 0.000007349217181477282

Nope. The next day:

Code:
0.000007349217181477282/7
= 0.000001049888168782468857

Nada. The next hour...

Code:
0.000001049888168782468857/24
= 0.000000043745340365936202375

Finally! That's a little over so let's rollback. It turns out the chances of you winning the lottery is about the same as you dying in the hour and a half... So if you buy the ticket more than 1.5 hours before the winners are declared, you have a higher chance of dying a road-accident related death than winning... Nice.

Here's another example: theweek.com did a calculation of the chances of dying in a plane crash. The chances of that happening is 1 in 11,000,000. Yeah, choke up your coffee. Trying to win the lottery and succeeding, is less, fucking, likely, than succeeding in trying to commit suicide by riding on a plane...

Fuck.

So how could you increase your chances of winning the lottery? The most obvious way is by buying a lot of tickets. Hehe. Easier said than done.

Buying 1,000,000 tickets (Cost: £2,000,000):
Code:
0.0000000715112384*1000000
= 0.0715112384

That's a 7% chance of winning. Nice, but not really worth it.

Buying 10,000,000 tickets (Cost: £20,000,000):
Code:
0.0000000715112384*10000000
= 0.715112384

That's a 71% chance. Are you willing to risk it?

Buying 14,000,000 tickets (Cost: £28,000,000):
Code:
0.0000000715112384*14000000
= 1.0011573376

That's just over a 100% chance, with a price tag of £28,000,000. Damn. BUT... The average jackpot is only £2,053,984. Congratulations. You just won the lottery and lost £26,000,000.

This thread took a long time. Feedback is appreciated.

RE: [Mathematics] Weird Lottery Probability - lux - 03-30-2015

Good shit. Now calculate the chance of me winning £10 from 4 correct numbers, etc.

Also, £1 for a UK lottery ticket, £2 for the EUROmillions, go calculate it with the whole of Europe.

But good shit myfriend.

RE: [Mathematics] Weird Lottery Probability - Eclipse - 03-30-2015

(03-30-2015, 09:39 PM)Lux Wrote: Good shit. Now calculate the chance of me winning £10 from 4 correct numbers, etc.

Also, £1 for a UK lottery ticket, £2 for the EUROmillions, go calculate it with the whole of Europe.

But good shit myfriend.

Thanks bby. <3

£2 apparently - http://www.bbc.co.uk/news/business-24369542
Other links brought up the same price.

RE: [Mathematics] Weird Lottery Probability - Satan - 03-30-2015

Of course in us you have kickers and addons to your lottery tickets (at least where I live) that add in a whole nother aspect of your chances of winning, but yeah. Close enough.

RE: [Mathematics] Weird Lottery Probability - Eclipse - 03-30-2015

(03-30-2015, 09:50 PM)Six Wrote: Of course in us you have kickers and addons to your lottery tickets (at least where I live) that add in a whole nother aspect of your chances of winning, but yeah. Close enough.

I've just done it for the basic backbone of the lottery. There are plenty of other variables here in the UK too: I just haven't included them.

RE: [Mathematics] Weird Lottery Probability - lux - 03-30-2015

(03-30-2015, 09:49 PM)Eclipse Wrote: Thanks bby. <3

£2 apparently - http://www.bbc.co.uk/news/business-24369542
Other links brought up the same price.

MOTHERFUCKERS, FUCK THAT, BRING BACK THE ONE POUND LOTTERY TICKET.

NIGE' WILL SORT THIS OUT, FUCKING IMMIGRANTS INFLATING MY GAMBLING.

RE: [Mathematics] Weird Lottery Probability - Satan - 03-30-2015

(03-30-2015, 09:58 PM)Eclipse Wrote: I've just done it for the basic backbone of the lottery. There are plenty of other variables here in the UK too: I just haven't included them.
Tl;dr version of whole thread: statistically you'll die on your way to cash that winning ticket.

RE: [Mathematics] Weird Lottery Probability - Eclipse - 03-30-2015

(03-30-2015, 10:03 PM)Lux Wrote: MOTHERFUCKERS, FUCK THAT, BRING BACK THE ONE POUND LOTTERY TICKET.

NIGE' WILL SORT THIS OUT, FUCKING IMMIGRANTS INFLATING MY GAMBLING.

Vouch.

(03-30-2015, 10:03 PM)Six Wrote: Tl;dr version of whole thread: statistically you'll die on your way to buy the ticket.

FIFY, but yeah.
It's funny that the only people that have replied are those that thought the Mathematics section was a bad idea. Kek.

RE: [Mathematics] Weird Lottery Probability - Master - 03-30-2015

You say that you need to buy a lot of tickets (14,000,000) to get 100% of the numbers right but Derren Brown only needs one.


RE: [Mathematics] Weird Lottery Probability - lux - 03-30-2015

(03-30-2015, 11:17 PM)Master Wrote: You say that you need to buy a lot of tickets (14,000,000) to get 100% of the numbers right but Derren Brown only needs one.
-snip-

Because that man is a bloody alien.