aka. Things That Everybody Should Know About Probabilities, part 1

One of my pet peeves is how bad people understand such concepts as randomness and probabilities (hey, gambling wouldn’t work so well otherwise). And I mean very basic stuff, you know. Classical combinatorics can be very hard even for mathematically talented people, as some famous puzzles like the Monty Hall problem demonstrate. But there are also very basic things that
many more mathematically challenged people understand, yet some highly educated people as doctors and others often fail to grasp. So I’ll post a short series, which will remain very short unless I get enough hits, each trying to debunk one myth related to probability, common enough to annoy me out of my mind. So, without further ado…

Myth #1: according to law of standard distribution, it is now more likely to have tails after 12 consecutive heads

This is a very general misconception and should be simple to understand properly: no laws of nature keep “tally count” of events and affect future outcomes respectively. Naturally, it is more likely to get roughly 10 tails and 10 heads in 20 consecutive coin flips than say, 20 consecutive heads, but if you have already flipped the coin 19 times and every one of them is heads (assuming the coin is “normal” and not manipulated in any ways to make the other option more likely), the next flip, the 20th, is just as likely to be heads as tails. The crucial point lies in the fact that throwing 19 consecutive heads is rather unlikely, but if you manage to accomplish such sequence, the next flip is like any other flip, totally unaffected by previous flips or history. You’d have 50% chance to get another heads, leading to 20 consecutive heads, or 19 heads and tails. Really.

Now, don’t say that “my luck has been so bad now that it has to turn to good”. With purely random events each event is independent from the others — otherwise it wouldn’t be completely random. It’s that simple. Now flame on.

Being inconsistent is next to being a doofus, and none of us wants to be one. So, you’ve probably applied the Grand Principle Of Consistency to insurances: you either have none (optional ones, I mean) or you simply exclamate a resounding yes! to almost every suggestion a telemarketer is apt to make to you.

Unless, of course, you have deduced some rules you always apply. Consistently.

Today I had an interesting discussion with my colleague. His suggestion was rather smart one, though simple (hey — many smart inventions are simple as an afterthought, no?). The suggestion was to pick those insurances which have relatively negligible costs AND cover you against damage which is Absolutely Inconvenient To Endure. Another proposition is that appropriate conditions and/or environment exists for the unwanted event to occur. Insurance against water or fire damage in a condominium is a good example. If you accidentally start a fire due to negligence destroying several other peoples’ property, the cost could be so high that your economy would be totally ruined. Then again, an anti-example would be the theft of your beloved mountain bike. I mean, it is now sooooooo shiny and nice to ride with Xenon lamps, carbon fiber wheels, GPS nav computer and whatnot, but after six years or so you’ll be ashamed of showing in public places with the bike because it would be then soooo 00′ies. Getting the bike stolen could be a disappointment in the scale from ε to ξ, the latter being somewhere in the neighborhood of getting your Aztec megalopolis Chihuahuatitlan devastated by the dastard attack of those puny, wretched French in Civilization 4, but not much more. I mean, you have to weigh the product <monetary loss due to theft of the bike> times <probability of the French making their move> against definite loss of monthly/annual money to Acme corp (dial 1-800-gullible-fool for our best offer) insurance company. Yeah.

An inverted principle along the same lines suggested by the friend — somewhat surprisingly due to bad odds — is that it is good to play lottery using negligible investment (yes, I’m very well aware of the phrase lottery is an added tax for the mathematically/probabilistically challenged). The idea is that spending something like 0.2 per cent of your net income to lottery your purchasing power is not diminished at all, whereas in the (extremely unlikely) event you can get gazillions of cash. Well, almost. I mean, Canon EOS-1Ds Mark III with some fine glass costs only so much, and hitting the jackpot in the lottery affords you at least 100 copies, even after taxes. Unless you’re stupid enough to pick a pattern (like your birthday) shared by thousands of other people.

I’d like to refine the principle, but at the moment I’m only able to refine the mentioned idea. Any suggestions?

Nevertheless, next time when you are negotiating with an insurance agent, even if you choose to ignore risk analysis and/or probabilities, remember that the real professionals behind the rates do know their Poisson distributions and eat standard deviations spiced with root mean squares on breakfast. Rest assured that all the tools they posses will be used against you. You’d be better off starting from the definition unless you haven’t yet.

Until recently, I have associated Apple products with reliability, power, simplicity and high amount of polish, extended from simply good products to support, maintenance and lifecycle.

Yup, I’ve noticed that no software is perfect, and Apple products are no exception. But somehow I have overlooked minor deficiencies so far because I have been able to meet my goals (which is the only thing that matters in the end) quickly with satisfying end result.

Alas, that was the Good Old Days, i.e. days before the Snow Leopard upgrade.

Now, I really like the idea of no new features, performance tweaks and all that is fine in the whitey cat release. But the amount of crashes is unacceptable. I mean, several crashes a day! Not even Vista or immature Linux distributions crash that often. And yes, I’ve applied the first SL update — it didn’t affect the crash problem.

Hopefully Apple will learn something and tests the release more thoroughly the next time.