To determine which event has the highest probability, let's analyze each option step by step.
Given the data from the table:
- Total buses observed: 110
Option A: The bus is from route [tex]\(C\)[/tex] and is delayed
- Number of delayed buses in route [tex]\(C\)[/tex]: 6
- Probability of selecting a bus from route [tex]\(C\)[/tex] that is delayed:
[tex]\[ \frac{6}{110} = 0.05454545454545454 \][/tex]
Option B: The bus is from route [tex]\(C\)[/tex] and is on time
- Number of on-time buses in route [tex]\(C\)[/tex]: 24
- Probability of selecting a bus from route [tex]\(C\)[/tex] that is on time:
[tex]\[ \frac{24}{110} = 0.21818181818181817 \][/tex]
Option C: The bus is from route [tex]\(B\)[/tex] and is delayed
- Number of delayed buses in route [tex]\(B\)[/tex]: 8
- Probability of selecting a bus from route [tex]\(B\)[/tex] that is delayed:
[tex]\[ \frac{8}{110} = 0.07272727272727272 \][/tex]
Option D: The bus is from route [tex]\(A\)[/tex] and is on time
- Number of on-time buses in route [tex]\(A\)[/tex]: 28
- Probability of selecting a bus from route [tex]\(A\)[/tex] that is on time:
[tex]\[ \frac{28}{110} = 0.2545454545454545 \][/tex]
Now, let's compare these probabilities:
- Probability of option A: 0.05454545454545454
- Probability of option B: 0.21818181818181817
- Probability of option C: 0.07272727272727272
- Probability of option D: 0.2545454545454545
The highest probability among these is [tex]\(0.2545454545454545\)[/tex], which corresponds to option D.
Therefore, the correct answer is:
D. The bus is from Route [tex]\(A\)[/tex] and is on time.
