Question

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Problem 2: Late for work Suppose that people commuting from Cambridge are typically late for work 5 days a month. We can say that the number of times Cantabrigians are late for work each month is a Poisson random variable with λ-5. The city changes the timing of one key traffic light encountered by 60% of Cambridge commuters in such a way that they typically are late for work only 3 days a month, while the remaining 40%, who don't go through that traffic light, are typically late 5 days a month as they were before. Part A: How likely is it that someone who does go through that traffic light will be late for work 2 times in the month following the timing change? Part B: How likely is it that someone who does not go through that traffic light will be late for work 2 times in the month following the timing change? Part C: Cantab Bob is late for work 2 times in the month following the timing change. Given that he was late 2 times, how likely is it that he goes through that traffic light on his daily commute?

Answer 1

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