5X5 Episode 56

Probability
S: This is the SGU 5X5 and tonight we're talking about.

E: Probably.

S: Probably. Not probably but probability. Mathematical probability is something that humans have an inherently a poor understanding of. We do not have a good mind for numbers or an intuitive sense of probability, especially when you start dealing with large numbers, and this causes people to form erroneous conclusions all the time.

R: Yeah, my favorite example of how we can't really understand probability is the example that if you have twenty-three people in a room together, what are the chances that two of them share a birthday? And a lot of people would think that the chances are very small when in fact they're greater than 50%. It's one of those things where, you know, it doesn't make sense at first but when you examine the, it makes perfect sense. Our intuition kind of leads us astray in that case.

E: Another example pertaining to the law of very large numbers and probability is that of lottery winners. You would think that the odds of a person winning a lottery jackpot twice in their lifetime would be something astronomical, maybe in the hundreds of millions, billions or trillions. But in actuality, the odds of a person winning two lottery jackpots is about one in thirty. The point there is&mdash;to remember is that, yeah, the odds of me, Evan, winning two jackpots in my lifetime is probably in the trillions but the odds of somebody, anybody, of all the people who play lottery, of all the people who have the possibility of buying lottery tickets, that whittles down to a small number, which is just one in thirty.

B: That's a good point, Evan. It's called the. It's a very important aspect of probability and statistics. Basically, this law says that truly bizarre coincidences are bound to happen when sample sizes get big enough, such as the millions of people playing lotto numbers. One of my favorite example is if you dream about a plane crash the night before a real one happens, you might think, "wow this must be precognition; I might be psychic," but consider that six billion people were dreaming last night, and probably a million of them all could have had dreams of plane crashes. Just from this law of truly large numbers, it's just bound to happen when you've got a sample size that is just so huge.

S: That's right. In the city of ten million people, a one-in-ten-million coincidence happen every day.

R: So you should never tell somebody that they're one in a million because, frankly, that's insulting them.

B/E: (laughs)

S: That's right.

E: It depends on where you live.

J: And this adding more proof to the fact that psychics don't exist because, statistically, some psychic should have guessed that 9-11 was going to happen and that didn't even happen.

S: And speaking of psychics, they depend upon poor intuitive sense of probability when they do their, 'cause they'll throw out a lot of guesses and some of them will hit and they'll count on the reader, the person being read, not only remembering the hits and forgetting the misses but grossly underestimating the probability that they would have gotten a few of those guesses correct by chance alone.

To follow up on the lottery example, Bob, that was a very, very good example; I think it's one that people can relate to... and also specifically, the difference between John Smith winning and the difference between just someone somewhere winning. In fact, this comes up a lot, for example, when creationists talk about the incredible improbability of evolution, they're making the lottery fallacy, the probability fallacy. They're assuming the probability of life as it exists now occurring by chance. Yes, that's very unlikely. Specific things evolving may be inherently unlikely, but the fact that something evolved is not unlikely at all. It's guaranteed, just as it's guaranteed that eventually someone's going to win the lottery.