You’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats...

Question

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1.

Now the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to switch and pick door No. 2?”

What would you do?

Answer 1

I would switch my choice to door no 2 because there is a 66.6667 percent chance of me finding a car there versus 33.3333 percent chance at door 1.

This is because initially it was 33.3333 percent chance of finding a car on all the doors. But after he reveals a fake door the probability of finding the car of the doors 2 and 3 is assumed by door 2 alone as at door 3 it's 0 now. Keep in mind though that our initial choice was made based on no additional information which we get after the first step of choosing a door and therefore door 1 probability remains unchanged even after the reveal.

For a better explanation google "The Monty Hall Problem".