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For a one-week period, three bus routes were observed. The results are shown in the table below.

\begin{tabular}{|l|l|l|l|}
\hline & On-Time & Delayed & Total \\
\hline Bus Route A & 28 & 7 & 35 \\
\hline Bus Route B & 37 & 8 & 45 \\
\hline Bus Route C & 24 & 6 & 30 \\
\hline Total & 89 & 21 & 110 \\
\hline
\end{tabular}

A bus is selected randomly. Which event has the highest probability?

A. The bus is from route [tex]$C$[/tex] and is delayed.
B. The bus is from route [tex]$B$[/tex] and is delayed.
C. The bus is from route [tex]$A$[/tex] and is on time.
D. The bus is from route [tex]$C$[/tex] and is on time.

Sagot :

GinnyAnsweridn
To determine which event has the highest probability, we need to calculate the probabilities associated with each of the specified events.

1. Probability that the bus is from route C and is delayed:
- The number of buses from route C that are delayed: 6
- Total number of buses: 110
- Probability: [tex]\(\frac{6}{110} \approx 0.0545\)[/tex]

2. Probability that the bus is from route B and is delayed:
- The number of buses from route B that are delayed: 8
- Total number of buses: 110
- Probability: [tex]\(\frac{8}{110} \approx 0.0727\)[/tex]

3. Probability that the bus is from route A and is on time:
- The number of buses from route A that are on time: 28
- Total number of buses: 110
- Probability: [tex]\(\frac{28}{110} \approx 0.2545\)[/tex]

4. Probability that the bus is from route C and is on time:
- The number of buses from route C that are on time: 24
- Total number of buses: 110
- Probability: [tex]\(\frac{24}{110} \approx 0.2182\)[/tex]

By comparing these probabilities, we observe that:

- The probability the bus is from route C and is delayed is approximately 0.0545.
- The probability the bus is from route B and is delayed is approximately 0.0727.
- The probability the bus is from route A and is on time is approximately 0.2545.
- The probability the bus is from route C and is on time is approximately 0.2182.

Among these probabilities, the highest one is 0.2545, which corresponds to the event that the bus is from route A and is on time.

Therefore, the event with the highest probability is:
C. The bus is from route [tex]\(A\)[/tex] and is on time.
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