Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena.The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of dice is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
John Size trains winners like pigeons poop on statues - it all just seems so natural and with such an air of inevitability.Wednesday, 28 March, 2012, 12:00am
Tonight's Jockey Challenge promises to be an absolute corker and, while usual favourites Douglas Whyte, Darren Beadman and Brett Prebble all have good claims, none boast an outstanding book, which assures them of victory in the point-score event.1 Dec 2010 - 12:00am
The weekend's international trial races - sorry but it still seems more appropriate than the thoroughly unimaginative Jockey Club Mile, Cup, Sprint etc - did their job to set up the Cathay Pacific Hong Kong International Races next month ahead of today's announcement of the invited runners.24 Nov 2010 - 12:00am
Hong Kong needs an Asian Games, just like Beijing needed the Olympics. Sports is a great way of pulling everyone together. Even our masters in Beijing believe this and let's hope the people say yes.
Alvin Sallay column
Sunday Morning Post, August 15 Aug 2010 - 12:00am
Sunday's favourite-fest will doubtless have been welcomed by the wider punting audience after enduring something of a dry run in March, but further investigation shows favourite bettors are not exactly having a boom season.24 Mar 2010 - 12:00am
Brett Prebble has the right book to go back-to-back in the Jockey Challenge after being heavily backed as clear winner in the Happy Valley contest on Wednesday night.10 Jan 2010 - 12:00am
With a full book brimming with quality chances, Brett Prebble is a worthy favourite once again for the Jockey Challenge at Sha Tin this afternoon.
The Australian was beaten at odds-on on international day in the Challenge, and again midweek after firming into favourite in in-play betting, but it's hard to go past him as first choice for the day's riding honours again.19 Dec 2009 - 12:00am
The wheel has been around more than once for Soaring Dragon, who made it two from three for John Moore yesterday in the style of a horse on his way up the ladder, but we have seen it before.
When Moore took over Soaring Dragon (Darren Beadman) last December, the gelding broke his maiden first-up with a four-length victory at Sha Tin that spelled progressive.12 Oct 2009 - 12:00am
Maths is essential
I think mathematics is a very important subject. We need to know our numbers no matter what career we choose.7 Sep 2009 - 12:00am
After a relatively quiet time by his high standards, Brett Prebble will firmly announce 'I'm back' by taking today's Jockey Challenge at the expense of odds-on favourite and arch-rival Douglas Whyte.10 Jan 2009 - 12:00am
Douglas Whyte showed himself to be human on Wednesday at Happy Valley when he was sent off a worthy odds-on favourite for the Jockey Challenge, but failed to salute after going winless for the night.20 Dec 2008 - 12:00am
The oddity about last night's Jockey Challenge betting was the missing name of one of the Valley's brightest lights - Brett Prebble.26 Nov 2008 - 12:00am
Jockey Challenge punters who backed Douglas Whyte on Sunday had to sweat through a countback before the favourite got the verdict over Alex Lai Hoi-wing, but it is hard to argue against throwing the winnings back on again tonight.4 Nov 2008 - 12:00am
Punters who have been burnt taking short odds on Douglas Whyte in the Jockey Challenge have been given no respite by the Jockey Club oddsmakers and the enigmatic Frenchman Eric Saint-Martin looks better value today.1 Oct 2008 - 12:00am
Jockey Challenge odds makers have declared tonight's Happy Valley meeting a match between the usual suspects in Brett Prebble and Douglas Whyte. But punters on the favourite might have a nervous wait to see if they collect, and slow and steady may win the race.25 Jun 2008 - 12:00am