The movie 21 Please explain the math.

[Coronita]

[quote]We have a contestant we’ll call him ‘TheBreeze’ aka
‘TB’.
TB choses door #1, the probability that TB chose the door with the car is 1/3 and, the probability that it is behind one of the other doors is 2/3. By showing TB one of doors #2 or #3 which does not hide the car but a goat (#2 for instance), the host is giving TB an good idea of what is behind those two doors. The probability is still 2/3 that one of them hides the car, but now you know which of the two it would be: Door 3.

The probability is still only 1/3 that the car is behind Door 1, but 2/3 that it is behind Door 3.

Anyone remember “Lets Make a Deal”?
[/quote]

Also known as the Monty Hall problem, an example of conditional probability.
http://en.wikipedia.org/wiki/Monty_Hall_problem
http://en.wikipedia.org/wiki/Conditional_probability

You can literally count the outcomes if you need to and figure out your odds are better if you switch to avoid the mathematical proof.

[Anonymous]

There are many ways to explain why your probability of winning the car is in fact 66.6%. I find this easiest to understand:

Here is the key: Given the rules, if you always switch your pick, your first choice will always determine if you win or not.

(1) If your 1st choice is a goat, you will always win the car. This is because the host will reveal the other goat so when you change, it will ALWAYS be to the car.

(2) If your 1st choice is the car, you will always lose. This is because the host will reveal a goat so when you change, it will ALWAYS be to the other goat.

Therefore: Since your odds of initially picking a goat are 66.6%, your odds of winning the car is the same – 66.6%.

Not the simplest concept to understand but, it is obviously true.

[Anonymous]

There are many ways to explain why your probability of winning the car is in fact 66.6%. I find this easiest to understand:

Here is the key: Given the rules, if you always switch your pick, your first choice will always determine if you win or not.

(1) If your 1st choice is a goat, you will always win the car. This is because the host will reveal the other goat so when you change, it will ALWAYS be to the car.

(2) If your 1st choice is the car, you will always lose. This is because the host will reveal a goat so when you change, it will ALWAYS be to the other goat.

Therefore: Since your odds of initially picking a goat are 66.6%, your odds of winning the car is the same – 66.6%.

Not the simplest concept to understand but, it is obviously true.

[Anonymous]

There are many ways to explain why your probability of winning the car is in fact 66.6%. I find this easiest to understand:

Here is the key: Given the rules, if you always switch your pick, your first choice will always determine if you win or not.

(1) If your 1st choice is a goat, you will always win the car. This is because the host will reveal the other goat so when you change, it will ALWAYS be to the car.

(2) If your 1st choice is the car, you will always lose. This is because the host will reveal a goat so when you change, it will ALWAYS be to the other goat.

Therefore: Since your odds of initially picking a goat are 66.6%, your odds of winning the car is the same – 66.6%.

Not the simplest concept to understand but, it is obviously true.

[Anonymous]

There are many ways to explain why your probability of winning the car is in fact 66.6%. I find this easiest to understand:

Here is the key: Given the rules, if you always switch your pick, your first choice will always determine if you win or not.

(1) If your 1st choice is a goat, you will always win the car. This is because the host will reveal the other goat so when you change, it will ALWAYS be to the car.

(2) If your 1st choice is the car, you will always lose. This is because the host will reveal a goat so when you change, it will ALWAYS be to the other goat.

Therefore: Since your odds of initially picking a goat are 66.6%, your odds of winning the car is the same – 66.6%.

Not the simplest concept to understand but, it is obviously true.

[Anonymous]

There are many ways to explain why your probability of winning the car is in fact 66.6%. I find this easiest to understand:

Here is the key: Given the rules, if you always switch your pick, your first choice will always determine if you win or not.

(1) If your 1st choice is a goat, you will always win the car. This is because the host will reveal the other goat so when you change, it will ALWAYS be to the car.

(2) If your 1st choice is the car, you will always lose. This is because the host will reveal a goat so when you change, it will ALWAYS be to the other goat.

Therefore: Since your odds of initially picking a goat are 66.6%, your odds of winning the car is the same – 66.6%.

Not the simplest concept to understand but, it is obviously true.

[meadandale]

Yep, 2/3 is correct. We studied this problem in probability.

I like Brian P’s description of the problem. Makes it clear why the answer is 2/3’s.

[meadandale]

Yep, 2/3 is correct. We studied this problem in probability.

I like Brian P’s description of the problem. Makes it clear why the answer is 2/3’s.

[meadandale]

Yep, 2/3 is correct. We studied this problem in probability.

I like Brian P’s description of the problem. Makes it clear why the answer is 2/3’s.

[meadandale]

Yep, 2/3 is correct. We studied this problem in probability.

I like Brian P’s description of the problem. Makes it clear why the answer is 2/3’s.

[meadandale]

Yep, 2/3 is correct. We studied this problem in probability.

I like Brian P’s description of the problem. Makes it clear why the answer is 2/3’s.

[ucodegen]

Oy vey..

It is assumed that the contestant is making a correct statement by saying “The contestant does decide to change from door number 1 to door #2. He states by changing from original chosen door #1 to door #2 his odds of winning the car increased to 66.7%.” He is not. He is showing a complete lack of understanding in probability. The gameshows do this to up the ‘excitement’ because otherwise the game is played out. It allows them to clock another 5+ minutes on the same stupid choice with everyone else yelling and screaming. What it does tell you is that the host knows where the car is and a good poker player may be able to bluff it out of the game show host by watching the hosts responses to potential choices.

Basically, on the initial selection: 1 correct out of 3, making the odds 33% that any particular choice is right.

After the choice, one of the potentials is removed by uncovering the goat. This makes 1 out of 2 possible or 50% any particular choice is right.

Whether the choice is;
1) He has already chosen one and gets to modify his choice
2) There is a new choice between two brand new doors…

It is the same thing. The underlying thing is that revealing what is under one of the doors does not alter what is behind any of the other doors. Also remember that the sum of probabilities on any single choice have to sum to 1 and you do not get to carry over probabilities from a previous run on to a new choice, in particular when a new piece of information is added (revealing of the goat).

I dare the doubters of this to write a program that allows you to pick one of three.. reveals one that it knows is not it and asks you to choose to keep your choice or switch. Track the frequency that the original choice is right versus switching was the right choice. The revealed choice in the first selection is not counted because it was not made by the person doing the selection.

And for a final nail:
Why would a gameshow give you a choice that could suddenly improve your odds dramatically and so easily, particularly since they have to foot the bill?

[ucodegen]

Oy vey..

It is assumed that the contestant is making a correct statement by saying “The contestant does decide to change from door number 1 to door #2. He states by changing from original chosen door #1 to door #2 his odds of winning the car increased to 66.7%.” He is not. He is showing a complete lack of understanding in probability. The gameshows do this to up the ‘excitement’ because otherwise the game is played out. It allows them to clock another 5+ minutes on the same stupid choice with everyone else yelling and screaming. What it does tell you is that the host knows where the car is and a good poker player may be able to bluff it out of the game show host by watching the hosts responses to potential choices.

Basically, on the initial selection: 1 correct out of 3, making the odds 33% that any particular choice is right.

After the choice, one of the potentials is removed by uncovering the goat. This makes 1 out of 2 possible or 50% any particular choice is right.

Whether the choice is;
1) He has already chosen one and gets to modify his choice
2) There is a new choice between two brand new doors…

It is the same thing. The underlying thing is that revealing what is under one of the doors does not alter what is behind any of the other doors. Also remember that the sum of probabilities on any single choice have to sum to 1 and you do not get to carry over probabilities from a previous run on to a new choice, in particular when a new piece of information is added (revealing of the goat).

I dare the doubters of this to write a program that allows you to pick one of three.. reveals one that it knows is not it and asks you to choose to keep your choice or switch. Track the frequency that the original choice is right versus switching was the right choice. The revealed choice in the first selection is not counted because it was not made by the person doing the selection.

And for a final nail:
Why would a gameshow give you a choice that could suddenly improve your odds dramatically and so easily, particularly since they have to foot the bill?

[ucodegen]

Oy vey..

It is assumed that the contestant is making a correct statement by saying “The contestant does decide to change from door number 1 to door #2. He states by changing from original chosen door #1 to door #2 his odds of winning the car increased to 66.7%.” He is not. He is showing a complete lack of understanding in probability. The gameshows do this to up the ‘excitement’ because otherwise the game is played out. It allows them to clock another 5+ minutes on the same stupid choice with everyone else yelling and screaming. What it does tell you is that the host knows where the car is and a good poker player may be able to bluff it out of the game show host by watching the hosts responses to potential choices.

Basically, on the initial selection: 1 correct out of 3, making the odds 33% that any particular choice is right.

After the choice, one of the potentials is removed by uncovering the goat. This makes 1 out of 2 possible or 50% any particular choice is right.

Whether the choice is;
1) He has already chosen one and gets to modify his choice
2) There is a new choice between two brand new doors…

It is the same thing. The underlying thing is that revealing what is under one of the doors does not alter what is behind any of the other doors. Also remember that the sum of probabilities on any single choice have to sum to 1 and you do not get to carry over probabilities from a previous run on to a new choice, in particular when a new piece of information is added (revealing of the goat).

I dare the doubters of this to write a program that allows you to pick one of three.. reveals one that it knows is not it and asks you to choose to keep your choice or switch. Track the frequency that the original choice is right versus switching was the right choice. The revealed choice in the first selection is not counted because it was not made by the person doing the selection.

And for a final nail:
Why would a gameshow give you a choice that could suddenly improve your odds dramatically and so easily, particularly since they have to foot the bill?

[ucodegen]

Oy vey..

It is assumed that the contestant is making a correct statement by saying “The contestant does decide to change from door number 1 to door #2. He states by changing from original chosen door #1 to door #2 his odds of winning the car increased to 66.7%.” He is not. He is showing a complete lack of understanding in probability. The gameshows do this to up the ‘excitement’ because otherwise the game is played out. It allows them to clock another 5+ minutes on the same stupid choice with everyone else yelling and screaming. What it does tell you is that the host knows where the car is and a good poker player may be able to bluff it out of the game show host by watching the hosts responses to potential choices.

Basically, on the initial selection: 1 correct out of 3, making the odds 33% that any particular choice is right.

After the choice, one of the potentials is removed by uncovering the goat. This makes 1 out of 2 possible or 50% any particular choice is right.

Whether the choice is;
1) He has already chosen one and gets to modify his choice
2) There is a new choice between two brand new doors…

It is the same thing. The underlying thing is that revealing what is under one of the doors does not alter what is behind any of the other doors. Also remember that the sum of probabilities on any single choice have to sum to 1 and you do not get to carry over probabilities from a previous run on to a new choice, in particular when a new piece of information is added (revealing of the goat).

I dare the doubters of this to write a program that allows you to pick one of three.. reveals one that it knows is not it and asks you to choose to keep your choice or switch. Track the frequency that the original choice is right versus switching was the right choice. The revealed choice in the first selection is not counted because it was not made by the person doing the selection.

And for a final nail:
Why would a gameshow give you a choice that could suddenly improve your odds dramatically and so easily, particularly since they have to foot the bill?

[Author]

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