Final answer:
The student's assumption that the probability is 0.5 is incorrect without additional data to support the 50/50 distribution. Probability calculations depend on the actual distribution of outcomes, which in the case of a uniformly distributed event, is based on the time ratio within the total time available.
Step-by-step explanation:
No, Thomas' claim that the probability of the school bus being on time is 0.5 just because there are two options (on time or late) is not correct. Probability is not always evenly distributed amongst all outcomes without considering the actual chances or frequency of those events occurring. In probability theory, the chances of an event happening are determined by how often that event is expected to happen relative to all possible outcomes. So without specific data to indicate that the school bus is on time as often as it is late, we cannot conclude the probability is 0.5.
In situations where the time to wait for a bus is uniformly distributed, calculating probability involves looking at the ratio of the specific range of time over the total time. For example, if the waiting time for a bus is uniformly distributed between zero and 15 minutes, the probability that a person waits fewer than 12.5 minutes is the ratio of 12.5 minutes to the total 15 minutes. Hence, it would be calculated as 12.5/15 = 0.8333 or 83.33%.