A person has a 0.5 probability of taking a train to work, a 0.3 probability of carpooling, and a 0.2 probability of walking. The probability of being late is 0.2 when taking the train, 0.1 when carpooling, and 0.05 when walking. What is the probability of taking the train and being on time, or walking and being on time?

Rationale

0.59 is the probability of taking the train and being on time, or walking and being on time.

To calculate the probability of being on time while taking the train or walking, we first find the probabilities of being on time for each mode of transport and then sum them up. The probability of taking the train and being on time is 0.5 * (1 - 0.2) = 0.4, and the probability of walking and being on time is 0.2 * (1 - 0.05) = 0.19. Adding these together gives us 0.4 + 0.19 = 0.59.

A (0.3) YOUR ANSWER

This value does not account for the total probabilities of being on time for either the train or walking. It mistakenly underestimates the likelihood by not considering the probabilities associated with both transport methods.

B (0.4) YOUR ANSWER

While this option represents the probability of taking the train and being on time (0.5 * 0.8), it fails to include the probability of being on time when walking. The total probability must combine both transport methods to reflect the full scenario.

C (0.45) YOUR ANSWER

This option does not accurately represent the probabilities involved. It incorrectly assumes a lower probability than the calculated total, failing to consider the complete probabilities of both taking the train and walking while being on time.

D (0.59) CORRECT

This choice is correct as it combines the probability of being on time after taking the train (0.4) with the probability of being on time after walking (0.19), leading to the accurate total of 0.59.

Conclusion

The probability of 0.59 captures the likelihood of being on time for either mode of transport—train or walking—by summing the relevant probabilities for both scenarios. Each transport method contributes to the overall probability, demonstrating that a comprehensive approach is necessary for accurate calculation in probabilistic problems.

0.59 is the probability of taking the train and being on time, or walking and being on time.

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