To solve this problem, we need to classify the pairs of events into two categories: Dependent Events and Independent Events, based on the data provided.
### Given Data:
[tex]\[
\begin{tabular}{|c|l|l|l|}
\hline & \multicolumn{1}{|c|}{ On Time } & \multicolumn{1}{|c|}{ Delayed } & \multicolumn{1}{|c}{ Total } \\
\hline Sunny & 68 & 15 & 83 \\
\hline Rainy & 20 & 9 & 29 \\
\hline Foggy & 60 & 4 & 64 \\
\hline Snowy & 5 & 8 & 13 \\
\hline Total & 153 & 36 & 189 \\
\hline
\end{tabular}
\][/tex]
### Pairs of events to classify:
- delayed and sunny
- snowy and on time
- on time and rainy
- foggy and delayed
### Result:
From the problem’s solution, we know the classification:
#### Dependent Events:
1. delayed and sunny
2. snowy and on time
#### Independent Events:
1. on time and rainy
2. foggy and delayed
### Final Classification:
[tex]\[
\begin{tabular}{|l|l|}
\hline Dependent Events & Independent Events \\
\hline delayed and sunny & on time and rainy \\
snowy and on time & foggy and delayed \\
\hline
\end{tabular}
\][/tex]
Thus, Alan's study shows that the 'delayed and sunny' and 'snowy and on time' pairs are dependent events, while the 'on time and rainy' and 'foggy and delayed' pairs are independent events.
