CALLING all number-crunchers. What are the odds on Boro getting an away trip in today's FA Cup fifth round draw? Yeah, yeah, I know, its 50/50, the simple probability of a random event with only two possible outcomes. I can do that one.
But Boro's ball coming out second in the FA blazers' bingo pairings would be the TENTH successive away draw in the competition. What do those acquainted with the mathematics of sequential coin-tossing reckon are the odds on that?
Here is the basic data. So far there have been nine random events with only two possible outcomes, and the outcomes all going the same way. Nine heads, if you will:
2003-04:
3rd rd - Notts County H
4th rd - Arsenal A
2004-05:
3rd rd - Notts County A
4th rd - Manchester Utd A
2005-06:
3rd rd - Nuneaton A
4th rd - Coventry A
5th rd - Preston A
6th rd - Charlton A
SF - West Ham (Neutral)
2006-07:
3rd rd - Hull City A
4th rd - Bristol City A
Now my maths is a bit rusty. When I sat down to work it out I was just going to multiply the odds on the basis that it was an accumulator with nine winners at evens (I was going to do it with one of those little thin blue pens with an anxiously chewed end for purposes of authenticity) but that didn't seem right. I made it half (x2) = 1, (x2) = 2 (x2) =4 and so on. Nine times took it to 256 and an away tie in the next round would make it 512-1, which would have been worth a daft quid of anyone's money, although if you offered me it back in January 2004 I'd have declined on the grounds that the scenario was ridiculously far-fetched.
But when I googled 'probability theory' I realised there was a strong probability (greater than 0 but less than 1) I had probably got this completely wrong . My brain started to hurt....
"The strong law of large numbers states that if X1, X2, X3, ... is an infinite sequence of random variables that are pairwise independent and identically distributed with E(|Xi|) < ∞ (and where the common expected value is μ), then....
That's way above my head, like an Alan Kernaghan clearance. So if there is anyone out there who knows their way around a calculator and can work it out for me I'd appreciate it.
**Using the wonders of the interweb I've just brushed up my maths and stats on this on.
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