The Monty Hall Problem

Logic Level 1

You are attempting to win a car. There are three doors in front of you, you are told that behind one is a car and behind the other two are goats. You are asked to pick a door, but before it is opened one of the two unchosen doors is opened to reveal a goat. You are then asked if you wish to swap your choice of door or stick with your original choice. What do you do to ensure you win the car?

It makes no difference, it's 50:50 Stick Swap

Adam Chapman by Adam Chapman , 24, United Kingdom

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3 solutions

Michael Mendrin
Jul 23, 2015

I'm never ENSURED of winning the car

7 Helpful 0 Interesting 0 Brilliant 0 Confused

You're spot on, apologies for wording it like that as it may throw people off the question! It should say "what should you do in order to attempt to gain the car?". Thanks for noticing that!

Adam Chapman - 5 years, 10 months ago

I feel as if the timing matters.

Think of it this way, looking at the three doors you have a 1/3 chance of picking the car, and then you pick a door. Whoopa! "Wait a second", the schmarmy goat/car salesman cries! And he opens one of the other two doors.

You see, the goat is revealed BEFORE you have a chance to open the original door, and this leaves you with a distinct choice between two doors.

Assuming that the probability of getting a goat is distributed evenly between these two doors, you basically have just reduced the possibilities.

But the physical fact is the same, you have two equally likely options and a choice between them, making it 50:50.

However, if the salesman knew which door had the goat, then it may change things.

Mikal Olsen - 5 years, 10 months ago
Adam Chapman
Jul 22, 2015

There are two options; swapping and not swapping. The original probablity of you picking the car or a goat first try is 1/3 or 2/3 respectively. Once the door revealing the goat is opened, you still only have a 1/3 probability of having the car and a 2/3 probability, however this time it is out of only two possible doors. You are more likely to pick a goat first try, therefore once the other goat is revealed you have a 2/3 probability to win the car by swapping.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

After that one goat is revealed than also we will have 1/2 proabability of getting a car not 2/3

Deepak kumar - 5 years, 10 months ago

after the goat is revealed you are left with two closed door with one having car behind it so probability becomes 1/2 now for picking the car or goat..... so after the goat is revealed you are equally likely to pick any of them........... discuss it with your teachers they will tell you

Ayush Mishra - 5 years, 10 months ago
Chester Robinson
Aug 3, 2015

It increases the probability of a win, but getting a goat is still possible.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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