To determine whether the given pairs of events are dependent or independent, we need to analyze the likely connections between the weather conditions and the bus's arrival time.
### Analysis of Pairings
1. Delayed and Sunny:
On sunny days, the chance of the bus being delayed might be relatively independent of the weather, considering that sunny weather usually does not have adverse conditions to delay a bus. However, it could be seen as dependent if we take into account unexpected factors such as road congestion which might be more common in good weather due to increased travel.
2. On Time and Rainy:
Rainy weather often leads to slower traffic and delays. Therefore, the punctuality of the bus can be greatly influenced by rainy conditions. Consequently, these are likely dependent events.
3. Foggy and Delayed:
Foggy conditions typically reduce visibility, which can lead to traffic slow-downs and bus delays. Given this, foggy weather and bus delays are likely dependent events.
4. Snowy and On Time:
Typically, snowy conditions would also lead to delays due to slippery roads and reduced visibility. However, if the bus consistently arrives on time despite snowy conditions, it may suggest that the bus's punctuality is not significantly affected by snowy weather, indicating an independent relationship.
### Categorization into Dependent and Independent Events
Based on this analysis, we can categorize the events as follows:
#### Dependent Events:
- Delayed and Sunny
- On Time and Rainy
- Foggy and Delayed
#### Independent Events:
- Snowy and On Time
### Final Table:
\begin{tabular}{|l|l|}
\hline Dependent Events & Independent Events \\
\hline delayed and sunny & snowy and on time \\
\hline on time and rainy & \\
\hline foggy and delayed & \\
\hline
\end{tabular}
