A commuter has a 0.4 probability of taking the bus to work, a 0.4 probability of driving a car, and a 0.2 probability of cycling. The probability of being late is 0.15 when taking the bus, 0.05 when driving a car, and 0.1 when cycling. What is the probability of taking the bus and being on time, or driving a car and being on time?

Rationale

0.72

To find the probability of being on time when taking the bus or driving a car, we must calculate the probabilities of each scenario and sum them. The probability of taking the bus and being on time is 0.4 * (1 - 0.15) = 0.34, and for driving a car, it is 0.4 * (1 - 0.05) = 0.38. Adding these two probabilities gives us 0.34 + 0.38 = 0.72.

A (0.28) YOUR ANSWER

This choice underestimates the probability of being on time. If we calculate the probabilities correctly, we find that the contributions from both transport methods yield a higher combined probability.

B (0.32) YOUR ANSWER

This option also does not accurately reflect the calculations. The calculation for being on time when taking the bus and driving a car results in a total that exceeds 0.32, making it an incorrect choice.

C (0.34) YOUR ANSWER

While this option reflects the probability of being on time when taking the bus only, it neglects the contribution from driving a car. Therefore, it does not represent the total probability of being on time for both scenarios combined.

D (0.72) CORRECT

This is the correct choice, as it accurately sums the probabilities of both scenarios: being on time when taking the bus (0.34) and being on time when driving a car (0.38). The total probability correctly accounts for both commuting options.

Conclusion

In this scenario, the probability of being on time when commuting by bus or car is crucial for understanding punctuality. By correctly calculating and summing the probabilities of being on time for both transport methods, we arrive at 0.72 as the final answer. This comprehensive approach ensures that all possible scenarios are accounted for in the overall timing probability.

0.72

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