To calculate \( P(A \text{ and } B) \), which represents the probability of both event A (on-time arrival) and event B (transportation by bus) occurring, you would need specific probabilities or data about events A and B.
If you are given the individual probabilities \( P(A) \), \( P(B) \), and possibly the conditional probability \( P(A|B) \) (the probability of A occurring given that B has occurred), you could use the following formulas based on the laws of probability:
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If A and B are independent events: \[ P(A \text{ and } B) = P(A) \times P(B) \]
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If you know \( P(A|B) \): \[ P(A \text{ and } B) = P(B) \times P(A|B) \]
Without the specific values for \( P(A) \) and \( P(B) \) or the conditional probability, it is not possible to provide a numerical answer.
Please provide the relevant probabilities or context so that I can help you calculate \( P(A \text{ and } B) \)!
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