33. A machine is used in a production process. From past data, it is known that 97% of the
time the machine is set up correctly. Furthermore, it is known that if the machine is set
up correctly, it produces 95% acceptable (non-defective) items. However, when it is set
up incorrectly, it produces only 40% acceptable items.
a. An item from the production line is selected. What is the probability that the
selected item is non-defective?
b. Given that the selected item is non-defective, what is the probability that the
machine is set up correctly?
c. What method of assigning probabilities was used here?
34. In a recent survey in a Statistics class, it was determined that only 60% of the students
attend class on Fridays. From past data it was noted that 98% of those who went to class
on Fridays pass the course, while only 20% of those who did not go to class on Fridays
passed the course.
a. What percentage of students is expected to pass the course?
b. Given that a person passes the course, what is the probability that he/she attended
classes on Fridays?
35. Thirty-five percent of the students who enroll in a statistics course go to the statistics
laboratory on a regular basis. Past data indicates that 40% of those students who use the
lab on a regular basis make a grade of B or better. On the other hand, 10% of students
who do not go to the lab on a regular basis make a grade of B or better. If a particular
student made an A, determine the probability that she or he used the lab on a regular
36. In a city, 60% of the residents live in houses and 40% of the residents live in apartments.
Of the people who live in houses, 20% own their own business. Of the people who live
in apartments, 10% own their own business. If a person owns his or her own business,
find the probability that he or she lives in a house.
37. A market study taken at a local sporting goods store showed that of 20 people questioned,
6 owned tents, 10 owned sleeping bags, 8 owned camping stoves, 4 owned both tents and
camping stoves, and 4 owned both sleeping bags and camping stoves. Let Event A =
owns a tent, Event B = owns a sleeping bag, Event C = owns a camping stove,
and Sample Space = 20 people questioned.