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.