Problem 1

A random sample of 200 adults taking MBA are classified below by sex and their grade level attained.

Education Male Female

First year 38 45

Second year 28 50

Third year 22 17

If a person is picked at random from this group, find the probability that

a.The person is a male, given that the person is a second year student

b.The person is not yeta third year student, given that the person is a female.

Problem 2

A machine produces parts that are either good (90%), slightly defective (2%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which can detect any part that is obviously defective and discard it. What is the probability that a part is good given that it passed the inspection machine (i.e., it is notobviously defective)?

Problem 3

Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random and without replacement. What is the probability that we are lucky and find both of the defective fuses in the first two tests?

Problem 4

A manufacturing firm employs three analytical plans for the design and development of a product. For cost reasons, all three are used at varying times. In fact, plans 1, 2, and 3 are used for 30%, 20%, and 50% of the products, respectively. The defect rate is different for the three procedures as follows:

p(d / p₁ )=0.01, p(d / p₂ )=0.03, p(d / p₃ )=0.02,

where is the probability of a defective product, given plan j. If a random product was observed and found to be defective, which plan was most likely used and thus responsible?

Problem 5

One half percent of the population has a particular 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.

Let D be the event that Joe has the disease. Let T be the event that Joe's test comes back positive

a.What is the probability that Joe (a random person) tests positive?

b. Joe just got the bad news that the test came back positive; what is the probability that Joe has the disease.