Is Probability Subjective?
The idea of probability is something one cannot define but is helpful nevertheless. The notion of things that we regard as probability are usually called events. An event would be something as simple as rolling a die, the event that there would or would not be any rain tomorrow, and the event that there could be another pandemic in the next 50 years.
So if you roll a die, would you know what the outcome is going to be? The universe, nature, and life are built in a way where everything you think can happen happens.
The first case of probability is the classical one which most schools and formal education teach you. For Example: Toss a fair die. There are six possible outcomes, and since the die is fair, each number will have an equal chance. In this case, the chances of the outcome you desire have the probability of 1/6 or P(A) = m/n. This concept is simple for many situations but is very limited. For example, toss a weighed die where you have finite outcomes but are not very equally likely.
The second case of probability is through some experiments (Empirical). For example, if we have a weighted die but do not know how it is weighted. We could get a probable idea of each outcome by tossing the die multiple times, and using the proportion of time we toss the die gives us the outcome of the estimated probability. Imagine tossing a die 10,000 times, and each time you get a better approximation of the actual probability of the event. The disadvantage of empirical probability is that it relies on experiments. Consider the price of your favorite stock going up in value tomorrow. The only possibility to imagine here for one is today and tomorrow. The other disadvantage of empirical probability is that one does not know how large (n) needs to be to satisfy a certain probability. Thus could be an endless cycle.
The third case of probability is Subjective probability (my favorite) is your belief (An Individual’s measure) that the event he/she thinks of is likely to occur. In other words, having an intuition or a hunch makes good sense. You can take the classical and the empirical approach, combine them, and the combination could be expanded upon and taken into perspective. The disadvantage to this is that it is very subjective. One individual’s probability may ultimately differ from another, and this makes it disturbing and uncomfortable. The second disadvantage of subjective probability is that it does not obey the law of COHERENCE. For example, if you believe that the price of your favorite stock is going up by 80% in 2 days, then to be coherent, you cannot believe that the probability of the same stock going down by 80% exists.
The fourth case of probability is through having a Unified perspective (Axiomatic). This means that the coherent conditions for subjective probability can be proved for classical and empirical conditions. In short, all three cases of probability are unified.
“0” is the most negligible probability, and “1” is the most significant probability that exists.
Every time an event occurs, the probability of that event occurring is 1.
If two events cannot coincide, they should be mutually exclusive. For example: If H is an event where “1 comes up on the die“ and B is an event where “4 comes up on the die,” then the union of H and B is the event where “the number that comes up on the die is either 1 or even. “
