Let's categorize the events from Alan's data into dependent and independent events based on the relationship between weather conditions and bus arrival times.
Dependent Events are those where one event directly influences the other.
Independent Events are those where one event does not have a direct impact on the other.
### Dependent Events
1. Snowy and on time: Weather conditions like snow can have a direct impact on whether the bus can arrive on time or not. Snow typically disrupts transportation, making it less likely for buses to be on time, hence if they are on time during snowy weather, this would indicate a special relationship.
2. Foggy and delayed: Fog can greatly affect visibility, which can cause delays in bus schedules. This indicates that delays can be directly influenced by foggy conditions.
### Independent Events
1. On time and rainy: Whether it rains or not, the bus can still adhere to its schedule and be on time. Since rain is common and often accounted for in regular schedules, it does not necessarily delay the bus.
2. Delayed and sunny: Similarly, a bus can be delayed even when the weather is sunny. Delays could be due to other reasons like traffic congestion, mechanical issues, etc., which are not impacted by sunny weather.
Based on this analysis, let's fill in the table:
\begin{tabular}{|l|l|}
\hline Dependent Events & Independent Events \\
\hline snowy and on time & on time and rainy \\
foggy and delayed & delayed and sunny \\
\hline
\end{tabular}
