Another way to make the switching
Another way to make the switching answer seem intuitive is to imagine the situation with 1000 doors, 999 goats, and still just one prize. You choose a door (1 in 1000 chance it’s the right door) and your host opens all the doors you didn’t choose, which have goats behind them (998 goats). Stick or switch? Obviously you have a 999 in 1000 chance of winning if you switch, even though as you make the choice there are two doors, one prize, and one goat like before. This variant highlights one of the key distractions in the original problemthe host knows where the prize is and acts accordingly to eliminate dud doors. You choose without knowing where the prize is, but given that the host acts knowing where the prize is, your decision to stick or switch should take that into account.
Part of the problem is that we are used to thinking about probabilities as things attached to objects or events in simple one-to-one correspondence. But probabilities are simply statements about what can be known about uncertain situations. The probabilities themselves can be affected by factors that don’t actually affect the objects or events they label (like base rates and, in this case, the game show host’s actions).
Evolutionary psychologists Leda Cosmides and John Tooby4 argue that we have evolved to deal with frequency information when making probability judgments, not to do abstract probability calculations. Probabilities are not available directly to perception, whereas how often something happens is. The availability of frequencies made it easier for our brains to make use of them as they evolved. Our evolved faculties handle probabilities better as frequencies because this is the format of the information as it is naturally present in the environment. Whether something occurs or not can be easily seen (is it raining or is it not raining, to take an example), and figuring out a frequency of this event is a simple matter of addition and comparison: comparing the number of rainy days against the number of days in spring would automatically give you a good idea whether this current day in spring is likely to be rainy or not. One-off probabilities aren’t like this; they are a cultural inventionand like a lot of cultural inventions, we still have difficulty dealing with them.
Taken from : Mind Hacks
