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In the Name of God بسم الله

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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, and 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 pick door No. 2?" Is it to your advantage to switch your choice?

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17 minutes ago, shadow_of_light said:

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, and 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 pick door No. 2?" Is it to your advantage to switch your choice?

Assuming the car is more valuable and the goal is to win the car instead of goats (personally I would rather have a herd of goats than a car) – it makes no difference whether you switch your choice or stick with door 1. The probability is the same, namely 50-50.

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7 hours ago, Cherub786 said:

Assuming the car is more valuable and the goal is to win the car instead of goats (personally I would rather have a herd of goats than a car) – it makes no difference whether you switch your choice or stick with door 1. The probability is the same, namely 50-50.

At first, it seems so but your answer is wrong.

Surprisingly, if you switch your choise, you will be more likely to win!!

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21 minutes ago, shadow_of_light said:

At first, it seems so but your answer is wrong.

Surprisingly, if you switch your choise, you will be more likely to win!!

Pardon me, I’m lousy at brain teasers. Perhaps you can explain how changing my choice will increase the probability of winning the car.

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5 hours ago, shadow_of_light said:

At first, it seems so but your answer is wrong.

Surprisingly, if you switch your choise, you will be more likely to win!!

Maybe, The idea of a 'herd' may also apply to the problem. A goat being a herd animal will likely be close to another goat, so doors 2 and 3 are more likely both goats in this scenario. Also, will be easier to handle onto the stage. A goat behind door #3 infers one more likely behind #2 than #1.

Now, if Monty opened door #2 and a goat is there, then using this 'herd' idea, it is 50-50 there is another goat behind doors 1 and 3.

 

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16 hours ago, Cherub786 said:

Pardon me, I’m lousy at brain teasers. Perhaps you can explain how changing my choice will increase the probability of winning the car.

The full answer is here:

https://en.m.wikipedia.org/wiki/Monty_Hall_problem

You choose the door no.1...you have 1/3 chance of winning the car and 2/3 chance of losing. After the host (knowing what is behind each door) opens the door 3, your chances dont change*. Your chance of losing is still 2/3 unless you change your choice (i.e, select door no. 2 or no.3, but number 3 has just been opened).

The link below explains it in another way:

https://www.businessinsider.com/the-monty-hall-problem-2013-3#-10

* because the host didnt randomly choose a door.

Edited by shadow_of_light
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