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- Among the adult population of a certain town 50 per cent are males. 60 per cent are wage earners and 50 per cent are., 45 years of-age or over, 10 per cent of the males are not wage-earners and 40'per cent Of the males are u1ll/er 45. Make the best possible inferenc~ about the limits within which the percentage of persons (male or female) of 45 years or over are wage- earners.7.-The 11colleges of interest to a high school senior include 4that are expensive (tuition more than $20,000 per year), 4that are far from home (more than 200 miles away), and 2that are both expensive and far from home. a. If the student decides to select a college that s not expensive and within 200 miles of home, how many selections are possible? b. If the student decides to attend a college that is not expensive and within 200 miles from home during his first two years of college, and then will transfer to a college that is not expensive but is far from home, how many selections of two colleges are possible?Suppose a man's occupation can be classified as professional, skilled worker, or unskilled worker. Suppose eighty percent of the sons of professional men are professionals, ten percent skilled workers, and ten percent unskilled workers. further suppose that sixty percent of the sons of skilled workers are skilled workers, twenty percent professional, and twenty percent unskilled. finally, in the case of unskilled workers, fifty percent of the sons are unskilled workers and twenty-five percent are in the other two categories. Assume each man has at least one son, and construct a Markov chain by tracing the occupation of a randomly selected son of a particular family over several generations. Construct the transition probabilities matrix. Find the probability that the randomly selected grandchild of an unskilled worker is a professional worker.
- A glazier buys his glass from four different manufacturers - Clearglass (10%),Strongpane (25%), Mirrorglass (30%) and Reflection (35%). In the past, the glazierhas found that 1% of Clearglass' product is cracked, 1.5% of Strongpane's productis cracked, and 2% of Mirrorglass' and Reflection's products are cracked. Theglazier removes the protective covering from a sheet of glass without looking at themanufacturer's name - in other words, it's a random choice. He finds the glass iscracked. What is the probability it was made by Mirrorglass?Consider a screening system that analyzes the luggage that is being loadedto a plane. Each package first goes through a screening device. If it passes the test there, then it is loaded to the plane. If it does not, the package goes to a second screening device. The procedure is similar for the second device: if the luggage passes the test, it is loaded to the plane, if it fails, it issent to a third device. Packages that passes the test at third device are loladed to the plane, the ones that fail are taken paprt and not loaded to the plane.The screening devices i = 1; 2; 3 are not perfect. For each device, there are two risks:– With probability pi, each device erroneously passes a bag that is dangerous, given that previous devices have correctly rejected the bag.– With probability qi, each device erroneously fails a harmless bag that previous devices have also erroneously failed.Assume that pi; qi > 0 What is the probability that a dangerous package will be loaded to the aircraft?…Construct a Venn Diagram for the scenario. Suppose that a total of 208 students are enrolled in a Math course which offers three classes under Instructor X, Instructor Y, and Instructor Z. 4 students are enrolled under all three instructors. 48 students are enrolled under Instructor. Y. Twice as many students are enrolled under Instructor Y and Z (but not Instructor X) as those who are enrolled under both Instructor Y and X (but not Instructor Z), and 4 times as many as those enrolled under all three instructors. 124 students are enrolled in Instructor Z. 27 students are not enrolled in any class. Students enrolled under both Instructor Y and Z (but not Instructor X) is exactly the same size as the students enrolled under both Instructor X and Z.
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- Assume that there are six final exam to be scheduled at a university. Suppose that the courses are numbered from 1 to 6. Supoose that the following pairs of courses have common students: 1 and 2, 1 and 5, 2 and 3, 3 and 4, 3 and 6, 4 and 5, 4 and 6, 5 and 6. The planning Office wants to Schedule exams so that no student has two exams at the same time. What is the smallest number of time slots that are necessary to achieve this?Assume that in a university with 1000 students, 200students are taking a course in mathematics, 300 aretaking a course in physics, and 50 students are takingboth. How many students are taking at least one of thosecourses? How many are taking none of those courses? Howmany students are taking only Mathematics?A television director has to schedule commercials during 6 time slots allocated to commercialsduring the national telecast of the first period of a Montréal Canadiens hockey game.(a) In how many ordered ways can the television director schedule 6 different commercialsduring the 6 time slots?(b) In how many ways can the television director fill the 6 time slots allocated tocommercials, if there are 4 different commercials, of which a given one is to be shown 3times while each of the others is to be shown once?(c) As in (b) except the commercial shown three times can’t be shown before or after itself(i.e., not consecutively). How many ways can the television director fill the 6 time slots?
