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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?

Door 1 | Door 2 | Door 3 | result if switching | result if staying |
---|---|---|---|---|

Car | Goat | Goat | Goat |
Car |

Goat | Car | Goat | Car |
Goat |

Goat | Goat | Car | Car |
Goat |

A player who stays with the initial choice wins in only one out of three of these equally likely possibilities, while a player who switches wins in two out of three. The probability of winning by staying with the initial choice is therefore 1/3, while the probability of winning by switching is 2/3.

When they open one of the doors, your choices drop to two doors BUT this didn’t not reduce the chances that the prize is behind a door you did not select.

In essence, the door that you did not select inherited the odds of holding the prize from the door that was opened.

So, your original door still has the 33% chance of having the prize, and the remaining closed door now has a 67% chance.

This is an unbelievable yet mathematically proved result, which became much famous from an awesome Movie 21.