Final answer:
The question examines why a correct prediction serves as good evidence in the context of probability. Such evidence is stronger if the predictor, like Eric, potentially influenced the event, contrary to the gambler's fallacy which assumes independent events are 'due' based on past occurrences.
Step-by-step explanation:
The question is about the concept of probability and why the prediction of an event can be considered strong evidence in certain scenarios. A prediction being correct strengthens the evidence if the predictor has inside knowledge about the outcome, like Eric possibly rigging a lottery. In mathematics, especially in the study of probability, the idea of independent events plays an essential role. Each lottery drawing is an independent event; the probability of winning does not change based on past draws.
The student's confusion may stem from a common misunderstanding known as the gambler's fallacy. This is the incorrect belief that if an event has not happened for a while, it is 'due' to happen, which isn't true for independent events such as lottery draws or coin flips. However, in the case of a prediction made before an event occurs, if the prediction turns out to be accurate, and it was made under suspicious circumstances (like Eric's case), it can indicate that the event was not truly random but influenced in some way. Therefore, a successful prediction under such circumstances is strong evidence because it aligns with the low probability of the predicted event occurring naturally combined with the context and potential motivations of the predictor.