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# tut8ans - COMP211 Data and System Modeling(PROB/STAT...

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Page 1 of 3 COMP211 Data and System Modeling (PROB/STAT) Tutorial (Week 8) -Answer 1) In the past year there were 30 days on which accidents occurred along a certain stretch of highway. Assume that the probability that an accident occurs on any one day is 30/365 and that each day is independent of the others. What is the probability that there will be no accidents during the first 2 weeks of January? What is the probability that the first accident occurs on 3 rd day? Solution: Label the result “accident on j th day” as “success at j th trial.” Thus each day corresponds to one Bernoulli trial. The waiting time until an accident is therefore geometrically distributed with p = 30/365; thus P(no accident during first 2 weeks of January) = P ( W > 14) = g46721− g2871g2868 g2871g2874g2873 g4673 g2869g2872 = 0.3010 P(the first accident occurs on 3 rd day) = P( W = 3 ) = g46721− g2871g2868 g2871g2874g2873 g4673 g2870 ( g2871g2868 g2871g2874g2873 ) = 0.0692 2) Let Y be the number of successes in n independent repetitions of a random experiment having the probability of success p=2/3. If n=3, compute P(2≤Y), if n=5, compute P(3≤Y)?

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