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(c) If the events in succeeding minutes are mutually independent, what is the probability that there will be no accident at this location in a year? Q7. At a major and minor street intersection, one finds that, out of every 100 gaps on the major street, 65 are acceptable, that is, large enough for a car arriving on the minor street to cross. When a vehicle arrives on the minor street: (a) What is the probability that the first gap is not an acceptable one? (b) What is the probability that the first two gaps are both unacceptable? (c) The first car has crossed the intersection. What is the probability that the second will be able to cross at the very next gap? Q8. A machine part may be selected from any of three manufacturers with probabilities 𝑝1= 0.25, 𝑝2= 0.5and 𝑝3= 0.25. The probabilities that it will function properly during a specified period of time are 0.2, 0.3, and 0.4, respectively, for the three manufacturers. Determine the probability that a randomly chosen machine part will function properly for the specified time period. Q9. Consider the possible failure of a transportation system to meet demand during rush hour. (a)Determine the probability that the system will fail.
Demand level P(level) P(system| level) Low 0.6 0 Medium 0.3 0.1 High 0.1 0.5 . Q10. A cancer diagnostic test is 95% accurate both on those who have cancer and on those who do not. If 0.005 of the population actually does have cancer, compute the probability that the test indicates that person has cancer.