A transit agency surveyed a sample of 160 commuters about their primary mode of transportation and whether they travel during peak commuting hours. The results are summarized in the table below.
| Commute Mode | Peak Hours | Off-Peak Hours | Total |
|---|---|---|---|
| Bus | 35 | 45 | 80 |
| Train | 55 | 25 | 80 |
| Total | 90 | 70 | 160 |
If a commuter who travels during peak hours is selected at random from those surveyed, what is the probability that the commuter's primary mode of transportation is the train?
- A
- Answer
- C
- D
Answer
The probability that the commuter's primary mode of transportation is the train, given they travel during peak hours, is .
The correct answer is . To find the probability that a selected commuter's primary mode of transportation is the train, given that they travel during peak hours, we must look only at the column representing peak-hour commuters. The total number of peak-hour commuters is . Among these commuters, the number whose primary mode of transportation is the train is . Therefore, the probability is , which simplifies to .
Step-by-Step Solution
Key Concept
Conditional Probability from a Two-Way Table