Probability question

rat_race

Hi -- two of us are having a debate here about probability. Would be very grateful if someone could help us out here.

One of us says that:

If a computer picked 5 random numbers from a set of between 1 and 1,000,000, there is as much chance of it picking 5 random numbers which are only 2, 3, or 4 numbers apart from the first (in any order, of course), as there is of picking 5 other numbers which are 1...n numbers apart.

For example: 6000,6004,6001,6002,6003 is as likely as 6000, 56,999, 211,812, 99,987, 992,346.


The other says:

No, there is less probablity of randomly picking 5 numbers that are only 2, 3, or 4 numbers apart because there is a relationship between those numbers in that they are 4 or less numbers apart, which dramatically reduces the probablilty.


Can someone clarify which one of us is right? Thanks!

locum-motion

If you look at the lottery thread, there's plenty of explanation as to why 1,2,3,4,5,6 is just as likely to come up as any other set of six numbers.

I reckon that's essentially the same question as you're asking.

Yakuza

Setting aside the fact that computers pick pseudorandom numbers (they follow an algorithm to pick the numbers, so they aren't truly random), and that you'd have to write a program to get it to pick several numbers without replacement from a set of numbers (i.e. you could, in theory, get the same number from a computer twice if you asked it several times to merely pick a number between a certain range), as locum-motion says, any group of numbers is equally likely to any other set.

If you ran such a simulation, given a uniformly distributed set of numbers, you might expect there to be large gaps between numbers, but from a probability point of view, one set is as likely as another.

As an aside, never play 1,2,3,4,5,6 in the lottery as if you win, you'll have to share it with the hundreds of gobsh1tes who gave no thought to the fact that other people may use the same numbers.

Look at this article from the other day in the IT : http://www.irishtimes.com/news/ireland/irish-news/six-lotto-jackpot-winners-means-getting-just-588-000-each-1.1661814

The most popular number sequence played in Saturday night’s draw was, incredibly, 1, 2, 3, 4, 5, and 6.

No fewer than 531 Lotto players played these numbers on Saturday, and if those numbers had been drawn on Saturday evening, each Lotto jackpot winner would be getting just over €6,645.

The second most popular number sequence played for Saturday evening’s draw was 5, 10, 15, 20, 25, and 30, and 455 Lotto players played these numbers. The jackpot prize payout per winner would have been just over €7,755 if these six numbers had come out of the drum on Saturday.

Never play 1,2,3,4,5,6 or 5,10,15,20,25,30 - it's not that you're any less likely to win, but you're most definitely going to share it with others. Imagine how you'd feel - having won €6,645 when your normal prize for winning is in the millions?