Question 2 (20 points): An engineering construction firm has three sales engineers. Engineers 1, 2 and 3 estimate the cost of 30%, 20%, and 50% respectively, of all the jobs bid by the company. For i = 1,2,3, define Ei, as the event that a job is estimated by engineer i. The following probabilities describe the rates at which the engineers make serious errors in estimating the costs. P(error|E1) = 0.01, P(error|E2) = 0.03 and P(error|E3) = 0.02 a) What is the total probability of a bid being erroneous? b) If a particular bid results in a serious error in estimating job cost, what is the probability that the error was made by engineer 1? c) If a particular bid results in a serious error, in estimating job cost, what is the probability that the error was made by engineer 2. d) If a particular bid results in a serious error, in estimating job cost, what is the probability that the error was made by engineer 3. e) Based on the solution of a-c, which of the engineers is most likely responsible for making serious errors?
Question 4 (20 points): Let X be the cost of all damages incurred in dollars following an auto accident. The company has discretized the cost into three categories represented by values 0, 1000, 5000 and 10000, which according to the company data occurs with the following probabilities: 0.8, 0.1, 0.08 and 0.02 respectively. a) Estimate the mean and the standard deviation of the cost of an accident b) The company offers a $500 deductible for any claimed accident. If the company wishes to make an expected profit of $100, estimate the value of premium that they should they charge?
Question 1 (20 points): a) If 50% of families subscribe to Netflix, 65% subscribe to Hulu and 85% subscribe to at least one of the two services, what percentage of families subscribe to both services? b) If the chance that workers named A and B will fail the professional exam is 50% and 20% respectively, also, if the chance that both will fail the exam is 10% i. Show from the above information that the two events are not mutually exclusive ii. Find the probability that at least one of them will fail the exam iii. Find the probability that Neither A Nor B will fail the exam
