Here's the easiest way I've found to convince people why switching is better:
Suppose instead of three doors, you have 100. There's a car behind one and goats behind 99 of them. You get to choose a door, and then 98 other incorrect doors will be eliminated.
So, you choose door 34. The host opens eliminates 1, 2, 3 ... 33, 35, 36... 85, and 87 through 100.
So either the prize is behind door 34, which you picked right off the bat, or 86, which is the only one the guy didn't open.
Intuitively, it's clear that they don't have the same probabilities of being correct, right? Essentially, you've always had a 1% chance of it being in 34, and the other 99% collapses into 86.
Suppose instead of three doors, you have 100. There's a car behind one and goats behind 99 of them. You get to choose a door, and then 98 other incorrect doors will be eliminated.
So, you choose door 34. The host opens eliminates 1, 2, 3 ... 33, 35, 36... 85, and 87 through 100.
So either the prize is behind door 34, which you picked right off the bat, or 86, which is the only one the guy didn't open.
Intuitively, it's clear that they don't have the same probabilities of being correct, right? Essentially, you've always had a 1% chance of it being in 34, and the other 99% collapses into 86.
How will we know, when the morning comes, we are still human? - 2D
Don't worry, my friend. If this be the end, then so shall it be.
Don't worry, my friend. If this be the end, then so shall it be.
