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

Answer 1

Monty Hall problem

When first choice is made, the probability of getting a car is 1/3 because you are making a aguess from 3 available choices. If you stick on to the same choice made, the probability of success does not change.

The host always elimminates a wrong option. Therefore, once after the host eliminating 1 of the 3 option. Therefore, whenever your initial selction is wrong then if you switch, you will win the car. The probability of initial selection being wrong is 2/3. Therefore, whenever you switch your probability of winning is 2/3.

Therefore, it is to your advantage to switch your choice of doors.