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Hi everyone,

2 goats and the car are from . The monkey is for you to remove from my back – it’s killing me!

The problem also was in “21” movie.

The setup is you are on a game show, there are 3 closed doors with 2 goats and a car behind the doors, you do not know what is behind which door, the host does. You sure want to get the car, not a goat. So it begins

1) you pick a door;

2) the host opens 1 of other 2 doors where a got is;

3) host gives you a choice to reconsider and pick the other closed door

Q: is the probability to get the car any different between the door you picked on step 1 and the other closed door?

A: door from step #1 has 1/3 probability to win, the other closed door has 2/3 probability to win (so, you always should changed your original choice to increase your chances).

I do understand why it is – the door from step #1 has 1/3 probability to win from the very beginning and the fact that another door is opened on step #2 doesn’t change this fact (from here you have 2/3 for the last door, because it’s the only door left at this moment).

The monkey on my back screaming that after step #3 you have a brand new fresh choice to make between just 2 doors, so probability must be ½ for each door. Please kill this damn monkey – it didn’t let me sleep last night. I’ve written a simple simulation that randomly places the car, makes my random choice, pretends the host opens a door with a goat and does or doesn’t change original choice. I ran it up to 100000 games for it always keeps the original pick and the same number of games where it always changes the original choice. The simulation confirms that 1st door wins in 1/3 of games and the last door wins in 2/3 of games (after 15-20 games the picture starts to show up, after 100 it’s already roughly about 1/3 and 2/3 and by 100000 games it’s even closer to 1/3 and 2/3). But the monkey doesn’t shut up! Help me!

Thanks.

2 goats and the car are from . The monkey is for you to remove from my back – it’s killing me!

The problem also was in “21” movie.

The setup is you are on a game show, there are 3 closed doors with 2 goats and a car behind the doors, you do not know what is behind which door, the host does. You sure want to get the car, not a goat. So it begins

1) you pick a door;

2) the host opens 1 of other 2 doors where a got is;

3) host gives you a choice to reconsider and pick the other closed door

Q: is the probability to get the car any different between the door you picked on step 1 and the other closed door?

A: door from step #1 has 1/3 probability to win, the other closed door has 2/3 probability to win (so, you always should changed your original choice to increase your chances).

I do understand why it is – the door from step #1 has 1/3 probability to win from the very beginning and the fact that another door is opened on step #2 doesn’t change this fact (from here you have 2/3 for the last door, because it’s the only door left at this moment).

The monkey on my back screaming that after step #3 you have a brand new fresh choice to make between just 2 doors, so probability must be ½ for each door. Please kill this damn monkey – it didn’t let me sleep last night. I’ve written a simple simulation that randomly places the car, makes my random choice, pretends the host opens a door with a goat and does or doesn’t change original choice. I ran it up to 100000 games for it always keeps the original pick and the same number of games where it always changes the original choice. The simulation confirms that 1st door wins in 1/3 of games and the last door wins in 2/3 of games (after 15-20 games the picture starts to show up, after 100 it’s already roughly about 1/3 and 2/3 and by 100000 games it’s even closer to 1/3 and 2/3). But the monkey doesn’t shut up! Help me!

Thanks.

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