Vos savant math problem

Question

Vos savant math problem, why would choosing to switch from door 1 to door 2 be better? In that specific scenario wouldnt it be 50/50 because of the host reveals a goat in door 3 then that means the only possible combinations are car goat goat or goat car goat

Answer 1

Hi Anna,

 

This is known as the "Monte Hall" problem. It is very counter-intuitive but true.

Let's say there are 3 options - Doors 1, 2 and 3. Behind one of the doors is a new car. There are goats behind the other two. You choose one of the doors, let's say door 3 (but it doesn't matter which one). The host opens door 1 and reveals a goat behind it. The host then gives you the opportunity to change your guess - do you want to stick with door 3 or change to door 2?

It turns out that the best choice is to change your guess. If you stick with your guess, the probability of winning is 1/3. But if you change your guess, the probability of winning is 2/3.

 

Think of it this way, the only time that it makes sense to stay with your original guess is i you were right the first time. The probability of being right the first time is 1/3. For the other 2/3 of the time (when your first guess was wrong), it makes more sense to switch.

 

Hope that helps. It's a very counter-intuitive, but true, finding. If you're interested in learning more, look up the "Monte Hall" problem.

Answer 2

You pick a door; the probability you did not get the car is 2/3. One of those 2 doors is opened and there is no car there but the probability that the car was behind one of those 2 doors is still 2/3. Therefore it makes sense to change doors.

 

This is a quick and dirty explanation. You can prove it also using probability calculations.

 

Let me know if that makes sense.