Probability after the fact and before the fact

I used to watch discovery channel a lot as a kid and there was a show where they would talk about the probability of some bizarre things. They would describe the event, like a snake hiding in the toilet pot of someone and biting the person on his genitals and then the person surviving. Then they would go on to calculate the probability of that event, it will be something like, the probability of snake hiding in toilet is 1/100000, then the chances of a person walking into the toilet when the snake was hiding is 1/100, he surviving after the attack is 1/1000, so the chances of the whole event happening is 1 in 10 billion or something. Then you’ll be left wondering if it is miracle or something that event even happened. There is an simpler explanation, the world is large and complex and there are trillions of rare but interesting things which might happen, some of those things do happen and the producers of the show go and find them. The probability of a particular rare event happening is low but the probability of some rare event happening is not.

This fooled by randomness effect happens in so many other areas too. Take Paul the Octopus for example, the one who used to predict result of football matches. He has been quite successful with his predictions and it unlikely that he might have got it by pure luck, right? Yes, it quite unlikely for Paul, in specific, to get the predictions right. But, Paul isn’t only one in the game. People keep trying to do such predictions with their pets and of all of these pets, someone will predict the right thing and that will come up in the news. Every pet who doesn’t predict the right result will be forgotten.