Is probability just relative to who or what is concerned?

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Mates

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For example, say two people are interested to know what two dice are going to reveal after being thrown. Bob closes his eyes and Tom covers one eye. Tom only sees one die and Bob doesn't see either. It would seem that there is a 1/36 chance of Bob guessing the outcome of the dice and a 1/6 chance of Tom knowing the outcome. So it would seem to me that probability is only relative to the observer concerned. Or put another way, probability is subjective.

Does this make sense?
 
I would not say that probability is "subjective" or "relative", and that you are confusing the probability of the event with the likelihood of a person being able to accurately predict an outcome.

For example, let's say that the outcome is 4 and 3.
1) The probability of this event occurring is 1/36.
2) The probability of Bob guessing correctly is also 1/36, but this is not affected by the probability of that throw, nor does it affect the probability of that throw occurring.
3) The probability of Tom guessing correctly is 1/6, but his simply means that he has more information than Bob, and has a better chance of guessing correctly what is on the other die. The probability of throwing a 4 and 3 is not affected by his extra information.
 
Actually, the mathematician Poincarre said something like probability is the measure of our ignorance.

Let's change your example a bit. There are three rooms. I roll one die in Room I. My assistant simultaneously rolls another dies in Room II, where Tom is, and the die comes up 3. Bob is in Room III. Tom should be willing to bet a dollar that the dice are respectively 3 and 4 if the payoff is 7 dollars. Bob should reject that bet. The difference is that Tom has more information.

There is a theory of subjective probability, but it is not a mathematical conjecture. Rather it is a proposed rule of rational behavior: if you have certain expected values after adjustment for risk, you should choose the highest expected value. The expected values are computed according to the rules of probability theory, but the the numbers derive from degrees of subjective belief and emotional weights related to risk rather than objective data.
 
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Mates said:
For example, say two people are interested to know what two dice are going to reveal after being thrown. Bob closes his eyes and Tom covers one eye. Tom only sees one die and Bob doesn't see either. It would seem that there is a 1/36 chance of Bob guessing the outcome of the dice and a 1/6 chance of Tom knowing the outcome. So it would seem to me that probability is only relative to the observer concerned. Or put another way, probability is subjective.

Does this make sense?
Click to expand...
There are subjective interpretations of probability, notably the Bayesian view. You can read about them starting here.
 
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