Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

1 in 14 million?

http://news.bbc.co.uk/1/hi/world/europe/8259801.stm

The Bulgarian authorities have ordered an investigation after the same six numbers were drawn in two consecutive rounds of the national lottery.

The numbers – 4, 15, 23, 24, 35 and 42 – were chosen by a machine live on television on 6 and 10 September.

An official of the Bulgarian lottery said manipulation was impossible.

A mathematician said the chance of the same six numbers coming up twice in a row was one in four million. But he said coincidences did happen.

I think 1 in 4 million is wrong. It should be 1 in 14 million (i.e. 1 in

). There must be a misprint in the BBC article.

What do you guys think?

Last edited by JaneFairfax (2009-10-03 23:14:25)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 1 in 14 million?

I'd imagine their mathematician did say 14 million, but the paper recorded it wrongly.
Edit: OK, MIF's article says the mathematician stated it as 4.2 million, so I'm wrong.

This isn't really the probability they want though. I don't know how long the Bulgarian lottery has been running, but considering the British lottery instead, there have been maybe 1000 draws since it started.

The probability of a repeat ever happening during that time is 1 in 14 thousand. Still low, but not as suspicious as before.

If we also assume that this would have been worldwide news if it had happened in any country's lottery, then it's reasonable to guess that this story was the first instance of it happening.

I'll take a blind stab at there being 100 countries with lotteries, each of them having done 1000 draws already.
This being the case, the chance of a repeat ever happening on any lottery since it started is now just 1 in 140.

With so many chances for this to happen, it was bound to happen eventually.
People focus on this one draw and view it with utmost suspicion, forgetting all the other draws when nothing exciting happened.

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Why did the vector cross the road?
It wanted to be normal.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: 1 in 14 million?

Good article: http://blogs.wsj.com/numbersguy/lottery-math-101-801/

We all know that random events like this can happen, and it is supposedly impossible to rig, but do they really know for sure? Could someone be playing with magnets or something more exotic, and it succeeded too well?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 1 in 14 million?

Hi Jane and all;

The Australian mathematicians agree with you. About a third of a page down.

http://www.abc.net.au/pm/content/2009/s2689394.htm

Mathsypersons analysis is right, since so many events would appear remakable the odds are much higher than you think. Also if it never happened it would definitely prove that the lottery was fixed.

This might explain the differences in the Bulgarian's calculation and the Australian's.

http://online.wsj.com/article/SB125366023562432131.html

Last edited by bobbym (2009-10-04 00:54:18)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.