Review Session1-2-3 - Review Session Selected problems from...

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Review Session Selected problems from Chapters 1, 2 and 3 Engineering Probability MTH 3301
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Problem 1- Independence A project consists of three independent tasks and the probabilities of these tasks being completed on time are .90, .80 and .95, respectively. Find the probabilities that: (i) All three tasks will be completed on time. (ii) The first two tasks will be completed on time and the third one will not. (iii) Either the first or last task will be completed on time.
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Problem 1- Independence Solution. Let Ci denote the event that task i is completed on time. The independence of the tasks translates into the independence of the events C1, C2, C3. Then by the definition of independent events, the first two probabilities are: 1- P(C1 and C2 and C3) = (.9)(.8)(.95) = 0.684 2- P(C1 and C2 and Cc 3) = ( .9)(.8)(.05) = 0.036 3- P(C1 UC3) = P(C1) + P(C3) - P(C1 and C3) = .9 + .95 - (.9)(.95) = 0.995.
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Problem 2- Conditional Probability The probabilities that a student in this class will expend a high, medium or low amount of effort in studying are .50, .30 and .20, respectively.
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