Does probability change with change in information about event?
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For example in the Monty Hall problem, initial probability of choosing a car behind three doors is 1/3. But as more information is available regarding a door not containing a car, the probability of the car being behind chosen door is 1/3 and other door is 2/3.
But to look at it another way, if there was another person who knew before hand that one of the doors contain a goat. Then for him, the probability of a car being behind one of the doors is only 1/2.
So, is probability subjective based on information available? It might seem obvious, but when we are taught probability, none of the theory address this point. Sure, they talk about the abstract concepts like independence, conditional probability but how they are tied to real world and their implications are rarely discussed.
probability
asked Aug 24 at 4:05
sunsun
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For example in the Monty Hall problem, initial probability of choosing a car behind three doors is 1/3. But as more information is available regarding a door not containing a car, the probability of the car being behind chosen door is 1/3 and other door is 2/3.
But to look at it another way, if there was another person who knew before hand that one of the doors contain a goat. Then for him, the probability of a car being behind one of the doors is only 1/2.
So, is probability subjective based on information available? It might seem obvious, but when we are taught probability, none of the theory address this point. Sure, they talk about the abstract concepts like independence, conditional probability but how they are tied to real world and their implications are rarely discussed.
probability
asked Aug 24 at 4:05
sunsun
33
I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46
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up vote
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favorite
For example in the Monty Hall problem, initial probability of choosing a car behind three doors is 1/3. But as more information is available regarding a door not containing a car, the probability of the car being behind chosen door is 1/3 and other door is 2/3.
But to look at it another way, if there was another person who knew before hand that one of the doors contain a goat. Then for him, the probability of a car being behind one of the doors is only 1/2.
So, is probability subjective based on information available? It might seem obvious, but when we are taught probability, none of the theory address this point. Sure, they talk about the abstract concepts like independence, conditional probability but how they are tied to real world and their implications are rarely discussed.
probability
asked Aug 24 at 4:05
sunsun
33
For example in the Monty Hall problem, initial probability of choosing a car behind three doors is 1/3. But as more information is available regarding a door not containing a car, the probability of the car being behind chosen door is 1/3 and other door is 2/3.
But to look at it another way, if there was another person who knew before hand that one of the doors contain a goat. Then for him, the probability of a car being behind one of the doors is only 1/2.
So, is probability subjective based on information available? It might seem obvious, but when we are taught probability, none of the theory address this point. Sure, they talk about the abstract concepts like independence, conditional probability but how they are tied to real world and their implications are rarely discussed.
probability
asked Aug 24 at 4:05
sunsun
33
asked Aug 24 at 4:05
sunsun
33
asked Aug 24 at 4:05
sunsun
33
asked Aug 24 at 4:05
sunsun
33
33
I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46
add a comment |Â
I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46
I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46
I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46
add a comment |Â
1 Answer
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1
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accepted
Probability is objective based on the information available. As Bayes taught us, such information depends upon prior information as well as evidence that comes in later. (Bayes teaches us the optimal method for incorporating both prior information and subsequent information.)
Indeed, if player 1 has no prior information, the probability of the car being behind each door is $1/3$. But for the other person who knows which door already contains a goat, the probability the car is behind one of the other (closed) doors is of course $1/2$.
Of course, given perfect information (such as host Monty Hall has), the probability the car is behind a particular door is either 100% (for the special door) and 0% behind each of the other doors.
This doesn't mean probability is "subjective," but just that it depends upon one's state of knowledge.
(There is a different technical meaning to the term "subjective probability," though. When you ask someone the chance of rain tomorrow and they say "30%," they are expressing a "subjective probability.")
answered Aug 24 at 4:28
David G. Stork
8,03121232
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Probability is objective based on the information available. As Bayes taught us, such information depends upon prior information as well as evidence that comes in later. (Bayes teaches us the optimal method for incorporating both prior information and subsequent information.)
Indeed, if player 1 has no prior information, the probability of the car being behind each door is $1/3$. But for the other person who knows which door already contains a goat, the probability the car is behind one of the other (closed) doors is of course $1/2$.
Of course, given perfect information (such as host Monty Hall has), the probability the car is behind a particular door is either 100% (for the special door) and 0% behind each of the other doors.
This doesn't mean probability is "subjective," but just that it depends upon one's state of knowledge.
(There is a different technical meaning to the term "subjective probability," though. When you ask someone the chance of rain tomorrow and they say "30%," they are expressing a "subjective probability.")
answered Aug 24 at 4:28
David G. Stork
8,03121232
add a comment |Â
up vote
1
down vote
accepted
Probability is objective based on the information available. As Bayes taught us, such information depends upon prior information as well as evidence that comes in later. (Bayes teaches us the optimal method for incorporating both prior information and subsequent information.)
Indeed, if player 1 has no prior information, the probability of the car being behind each door is $1/3$. But for the other person who knows which door already contains a goat, the probability the car is behind one of the other (closed) doors is of course $1/2$.
Of course, given perfect information (such as host Monty Hall has), the probability the car is behind a particular door is either 100% (for the special door) and 0% behind each of the other doors.
This doesn't mean probability is "subjective," but just that it depends upon one's state of knowledge.
(There is a different technical meaning to the term "subjective probability," though. When you ask someone the chance of rain tomorrow and they say "30%," they are expressing a "subjective probability.")
answered Aug 24 at 4:28
David G. Stork
8,03121232
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Probability is objective based on the information available. As Bayes taught us, such information depends upon prior information as well as evidence that comes in later. (Bayes teaches us the optimal method for incorporating both prior information and subsequent information.)
Indeed, if player 1 has no prior information, the probability of the car being behind each door is $1/3$. But for the other person who knows which door already contains a goat, the probability the car is behind one of the other (closed) doors is of course $1/2$.
Of course, given perfect information (such as host Monty Hall has), the probability the car is behind a particular door is either 100% (for the special door) and 0% behind each of the other doors.
This doesn't mean probability is "subjective," but just that it depends upon one's state of knowledge.
(There is a different technical meaning to the term "subjective probability," though. When you ask someone the chance of rain tomorrow and they say "30%," they are expressing a "subjective probability.")
answered Aug 24 at 4:28
David G. Stork
8,03121232
Probability is objective based on the information available. As Bayes taught us, such information depends upon prior information as well as evidence that comes in later. (Bayes teaches us the optimal method for incorporating both prior information and subsequent information.)
Indeed, if player 1 has no prior information, the probability of the car being behind each door is $1/3$. But for the other person who knows which door already contains a goat, the probability the car is behind one of the other (closed) doors is of course $1/2$.
Of course, given perfect information (such as host Monty Hall has), the probability the car is behind a particular door is either 100% (for the special door) and 0% behind each of the other doors.
This doesn't mean probability is "subjective," but just that it depends upon one's state of knowledge.
(There is a different technical meaning to the term "subjective probability," though. When you ask someone the chance of rain tomorrow and they say "30%," they are expressing a "subjective probability.")
answered Aug 24 at 4:28
David G. Stork
8,03121232
answered Aug 24 at 4:28
David G. Stork
8,03121232
answered Aug 24 at 4:28
David G. Stork
8,03121232
answered Aug 24 at 4:28
David G. Stork
8,03121232
8,03121232
add a comment |Â
add a comment |Â
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I don't think the problems are described clearly enough for me to follow. The Monty Hall problem is famous and I can fill in details on my own for that, but I have no idea what the problem structure is with the goat. It may also be helpful to be more precise about what you mean by "information available" and "none of the theory address this point." It may be the case that the existing definitions serve the purpose you want. If you try to be more precise about your objections and goals, you may come to appreciate the existing definitions as being more powerful than you realize.
– Michael
Aug 24 at 4:46