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Bob and Alice are to meet for lunch. Suppose that Bob's arrival time is a uniform random variable on the interval from 12:00 to 12:20

Bob and Alice are to meet for lunch. Suppose that Bob's arrival time is a uniform random variable on the interval from 12:00 to 12:20 and Alice's arrival time is a uniform random variable on the interval from 12:10 to 12:30. Assume that the two arrival times are independent. Calculate the probability that

(i) Alice arrives first.

(ii) Alice arrives at least 5 minutes later than Bob.

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