Select the correct answer.
For a one-week period, three bus routes were observed. The results are shown in the table below.
| | On-Time | Delayed | Total |
| :---------- | :------ | :------ | :---- |
| Bus Route A | 28 | 7 | 35 |
| Bus Route B | 37 | 8 | 45 |
| Bus Route C | 24 | 6 | 30 |
| Total | 89 | 21 | 110 |
A bus is selected randomly. Which event has the highest probability?
A. The bus is from route A and is on time.
B. The bus is from route C and is delayed.
C. The bus is from route C and is on time.
D. The bus is from route B and is delayed.
Answer (2)
Calculate the probability of each event: A ( 110 28 ), B ( 110 6 ), C ( 110 24 ), and D ( 110 8 ).
Compare the probabilities: \frac{24}{110} > \frac{8}{110} > \frac{6}{110}"> 110 28 > 110 24 > 110 8 > 110 6 .
Event A (bus from route A and on time) has the highest probability.
The event with the highest probability is: A .
Explanation
Understand the problem We are given a table showing the number of on-time and delayed buses for three routes: A, B, and C. We want to find which of the given events has the highest probability when a bus is selected randomly. The total number of buses observed is 110.
Calculate probabilities To find the probability of each event, we divide the number of occurrences of the event by the total number of buses (110).
Calculate each probability Event A: The bus is from route A and is on time. The number of buses from route A that are on time is 28. So, the probability of event A is: P ( A ) = 110 28 ≈ 0.2545 Event B: The bus is from route C and is delayed. The number of buses from route C that are delayed is 6. So, the probability of event B is: P ( B ) = 110 6 ≈ 0.0545 Event C: The bus is from route C and is on time. The number of buses from route C that are on time is 24. So, the probability of event C is: P ( C ) = 110 24 ≈ 0.2182 Event D: The bus is from route B and is delayed. The number of buses from route B that are delayed is 8. So, the probability of event D is: P ( D ) = 110 8 ≈ 0.0727
Compare probabilities and conclude Comparing the probabilities, we have: P ( A ) ≈ 0.2545 P ( B ) ≈ 0.0545 P ( C ) ≈ 0.2182 P ( D ) ≈ 0.0727 Since 0.2182 > 0.0727 > 0.0545"> 0.2545 > 0.2182 > 0.0727 > 0.0545 , event A has the highest probability.
Examples
This type of probability calculation is useful in many real-world scenarios, such as analyzing the reliability of different transportation routes or assessing the success rates of various business strategies. For example, a company might track the on-time delivery rates of different shipping companies to determine which one is the most reliable. Similarly, a marketing team might analyze the success rates of different advertising campaigns to identify the most effective strategies. By calculating and comparing probabilities, we can make informed decisions and optimize our outcomes.
The event with the highest probability is event A, which states that the bus is from route A and is on time, with a probability of approximately 0.2545. Other events have lower probabilities when compared. Thus, option A is the correct answer.
;
