Question Three () Suppose B. constitute a partition of the sample Space S and A an event defined on the same sample space such that MB)-for-I, . 2. B and M6- Show that 10 1PIAA) and write down the results for MRI MRI, and JO (%) A designer buys fabric from 2 suppliers. Supplier A provides 60% of the fabric, Supplier B provides the remaining 40%. Supplier A has a defect rate of 5%. Supplier B has a defect rate of 8%. Draw a tree diagram to illustrate the above information b. Calculate the probability of getting a good fabric. Given that a batch of fabric is good, what is the probability that it came from Supplier A? 1. Given that a batch of fabric is defective, what is the probability that it came from Supplier A? (b) ( ) A manufacturing firm employs three analytical plans for the design and development of a particular product. For cost reasons, all three are used at varying times. In fact, plans 1, 2and 3 are used for 30%, 20%, and 50% of the products respectively. The "defect rate is different for the three procedures as follows: ADP) -0.01 PDP)-000 where PDP) is the probability of a defective product, given plan /. If a random product was observed and found to be defective, which plan was most likely used and thus responsible? In a factory, machines, and produce electronic components. Machine produces 16% of the components, machine produces 50% of the components and machine produces the rest. Some of the components are defective. Machine produces 4%, machine 3% and machine 7% defective components. Draw a tree diagram to represent this information Find the probability that a randomly selected component is (by produced by machine and is defective (c) defective ( Given that a randomly selected component is defective, which machine is likely to have produced (c) () One half percent of the population in certain village has the EBOLA disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time. a. What is the probability that a person tests positive? b. A particular person just got the bad news that the test is positive what is the secilit at the person has Question Three () Suppose B. constitute a partition of the sample Space S and A an event defined on the same sample space such that MB)-for-I, . 2. B and M6- Show that 10 1PIAA) and write down the results for MRI MRI, and JO (%) A designer buys fabric from 2 suppliers. Supplier A provides 60% of the fabric, Supplier B provides the remaining 40%. Supplier A has a defect rate of 5%. Supplier B has a defect rate of 8%. Draw a tree diagram to illustrate the above information b. Calculate the probability of getting a good fabric. Given that a batch of fabric is good, what is the probability that it came from Supplier A? 1. Given that a batch of fabric is defective, what is the probability that it came from Supplier A? (b) ( ) A manufacturing firm employs three analytical plans for the design and development of a particular product. For cost reasons, all three are used at varying times. In fact, plans 1, 2and 3 are used for 30%, 20%, and 50% of the products respectively. The "defect rate is different for the three procedures as follows: ADP) -0.01 PDP)-000 where PDP) is the probability of a defective product, given plan /. If a random product was observed and found to be defective, which plan was most likely used and thus responsible? In a factory, machines, and produce electronic components. Machine produces 16% of the components, machine produces 50% of the components and machine produces the rest. Some of the components are defective. Machine produces 4%, machine 3% and machine 7% defective components. Draw a tree diagram to represent this information Find the probability that a randomly selected component is (by produced by machine and is defective (c) defective ( Given that a randomly selected component is defective, which machine is likely to have produced (c) () One half percent of the population in certain village has the EBOLA disease. A test is developed for the disease. The test gives a false positive 3% of the time and a false negative 2% of the time. a. What is the probability that a person tests positive? b. A particular person just got the bad news that the test is positive what is the secilit at the person has
