A forecast says there is a 30% chance of rain tomorrow. Tomorrow happens once. Two readings of probability disagree about what the number is about: a long-run frequency of similar days, or a degree of belief held now. The chapter shows that the arithmetic is shared and that each reading pays a price: the frequency reading needs repetitions the world may not supply, and the belief reading needs a prior that the evidence may not settle.
Take a position. Which reading should govern a single-event forecast, and what should the number be allowed to promise? In your answer: state the reading you choose and what it makes the number refer to; say how you would check the forecaster over many days, and what that check can and cannot establish about tomorrow; say what the prior is and how you would defend it; and name one way your position could mislead someone who follows it correctly.
Rubric. Tick each criterion your answer meets, then save the self-assessment. The platform does not grade it.
Worked solution
There is no single correct answer, so this is a model of the shape a complete answer takes. A level-3 answer might choose the belief reading and say that the 30% is the forecaster's degree of belief, held now, about a proposition that will be settled once. It then says how to check the forecaster without pretending that tomorrow is repeated: collect many forecasts, group them by announced rate, and compare the observed frequency in each group with the announced value. A forecaster whose 30% days are wet about 30% of the time is calibrated over that sequence. The check can support or weaken trust in the forecaster, and it cannot certify the single forecast, because the sequence is made of many days and tomorrow is one draw from it. The answer then names the prior: the forecaster's earlier record, the season, and the local climate, and it says what new evidence would move the number. It names a failure: a forecaster who always announces the base rate for the season is well calibrated and says nothing about tomorrow, so calibration alone does not make a forecast useful. A strong answer also states what the frequency reading would say, namely that the number refers to a reference class of days judged exchangeable with tomorrow, and that the choice of reference class is itself a modelling decision. The answer that scores 0 says only that tomorrow happens once and stops there.