The fascination of Maths thread

[Chantho]

I was reading Sasguru's book last night - lovely chapter on German lottery. They also draw 6 numbers out of 49. so ~ 1 in 14,000,000 of winning.

After ~3600 draws thhey got a repeat of numbers. It is like the birthday problem (23 people to have 50/50 chance of repeat) but using 14,000,000 and 3600 instead of 365 and 23.

The odds on the lottery were about 25%. I was quite stunned. I must work out the full details later and post them here...

The number of draws to get a 50% chance of repeat is about 4400, there is an exact formula (which I've forgotten) but a reasonable approximation is the square root of (n times the square root of 2) where n is the number of possible outcomes.

[AtW]

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[Diver]

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[pisces]

The good thing about numbers is that they go on forever so they never get boring

[Diver]

The good thing about numbers is that they go on forever so they never get boring

Oh god! I feel another counting thread coming on

[OwlHoot]

The good thing about numbers is that they go on forever so they never get boring

Integers certainly aren't boring, and you can even prove it: If not, and some positive integers were boring then there'd be a minimum boring integer. But that in itself would make it interesting, which is a contradiction.

Same thing applies to rational fractions, as these can be put in one-to-one correspondence with integers. But there may be some tedious real numbers.

[BrilloPad]

Oh god! I feel another counting thread coming on

in hex? binary? octal? latin? in words(e.g. one)?

[TimberWolf]

I was reading Sasguru's book last night - lovely chapter on German lottery. They also draw 6 numbers out of 49. so ~ 1 in 14,000,000 of winning.

After ~3600 draws thhey got a repeat of numbers. It is like the birthday problem (23 people to have 50/50 chance of repeat) but using 14,000,000 and 3600 instead of 365 and 23.

The odds on the lottery were about 25%. I was quite stunned. I must work out the full details later and post them here...

Likewise if you use a random set of numbers each week, after about 4000 draws you’ll have an even chance that the numbers you pick or are drawn one week will match one of your old set of 4000 numbers. You can then say ‘if only’ etc.

[KathyWoolfe]

Likewise if you use a random set of numbers each week, after about 4000 draws you’ll have an even chance that the numbers you pick or are drawn one week will match one of your old set of 4000 numbers. You can then say ‘if only’ etc.

yeah, but which one of the old set of numbers?

[TimberWolf]

yeah, but which one of the old set of numbers?

Last weeks, by Murphy's law. Statistically no previous draw is any more likely to come up again than any other though, assuming randomness. Any more than two particular people chosen in a room of people 23 would be the ones who have an even chance of sharing a birthday.