Le probabilità fisiche, che sono anche chiamate probabilità oggettive o di frequenza, sono associate a sistemi fisici casuali come la roulette, i dadi e gli atomi radioattivi. In tali sistemi, un determinato tipo di evento (come l'uscita di un sei nei dadi) tende a verificarsi con una percentuale continua o a 'frequenza relativa', in un lungo periodo di prove. Le probabilità fisiche spiegano, o sono chiamate a spiegare, queste frequenze stabili. Così parlare di probabilità fisica ha senso solo quando si tratta di esperimenti casuali ben definiti. I due tipi principali di teoria della probabilità fisica sono i conti di frequentista (come Venn) e i conti di propensione.
Relative frequencies are always between 0% (the event essentially never happens) and 100% (the event essentially always happens), so in this theory as well, probabilities are between 0% and 100%. According to the Frequency Theory of Probability, what it means to say that "the probability that A occurs is p%" is that if you repeat the experiment over and over again, independently and under essentially identical conditions, the percentage of the time that A occurs will converge to p. For example, under the Frequency Theory, to say that the chance that a coin lands heads is 50% means that if you toss the coin over and over again, independently, the ratio of the number of times the coin lands heads to the total number of tosses approaches a limiting value of 50% as the number of tosses grows. Because the ratio of heads to tosses is always between 0% and 100%, when the probability exists it must be between 0% and 100%.
In the Subjective Theory of Probability, probability measures the speaker's "degree of belief" that the event will occur, on a scale of 0% (complete disbelief that the event will happen) to 100% (certainty that the event will happen). According to the Subjective Theory, what it means for me to say that "the probability that A occurs is 2/3" is that I believe that A will happen twice as strongly as I believe that A will not happen. The Subjective Theory is particularly useful in assigning meaning to the probability of events that in principle can occur only once. For example, how might one assign meaning to a statement like "there is a 25% chance of an earthquake on the San Andreas fault with magnitude 8 or larger before 2050?" (See Freedman and Stark, 2003, for more discussion of theories of probability and their application to earthquakes.) It is very hard to use either the Theory of Equally Likely Outcomes or the Frequency Theory to make sense of the assertion.
Bayesians, however, assign probabilities to any statement whatsoever, even when no random process is involved. Probability, for a Bayesian, is a way to represent an individual's degree of belief in a statement, given the evidence.