1. ## Game show problem

This is a great puzzle that is almost always missed on the first try and even not accepted to be true after given proof of the answer. If you know the answer (it's a famous problem) please don't spoil it for others. Put your answer in the spoiler tags.

[spoiler]Use these tags to make this sentence hidden like below[/spoiler]

Spoiler:
Use these tags to make this sentence hidden like below

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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

2. Originally Posted by Jameson
This is a great puzzle that is almost always missed on the first try and even not accepted to be true after given proof of the answer. If you know the answer (it's a famous problem) please don't spoil it for others. Put your answer in the spoiler tags.

[spoiler]Use these tags to make this sentence hidden like below[/spoiler]

Spoiler:
Use these tags to make this sentence hidden like below

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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?
Spoiler:

3. Removing...

4. Spoiler:
It is advatageous to change the choice

5. Spoiler:

Sure Rajesh; at first, probability was 2/3; now 1/2.