Definition
The reference class problem is the difficulty that a probability statement about a particular thing has no determinate value until you specify which class of similar things you are counting it among. The same individual can belong to many classes at once, and each yields a different number.
Probability on the frequency interpretation is a ratio: how often a property shows up within a class. But every event sits inside indefinitely many classes, so the choice of class — the reference class — is not given by the event itself. Pick a different class and the probability shifts.
Why it matters
How it works
Suppose you want the probability that a specific person lives to 80. As a member of the class "humans" the figure is one value; as a member of "humans who smoke" it is lower; as a member of "humans who smoke but run marathons" it shifts again. Each class is real, and each frequency is correct for that class — yet they disagree about the one person.
There is no purely logical rule that picks the right class. Priest treats this as evidence that the frequency interpretation cannot, on its own, deliver the single-case probabilities that everyday reasoning demands. The usual practical fix — choose the narrowest class for which you still have reliable data — is a pragmatic compromise, not a solution.