Applied Statistics and Probability for Engineers, 7th edition 2017
Let R denote the event that a product exhibits surface roughness. Let N, A, and W denote the events that the blades are
new, average, and worn, respectively. Then,
2.6.6. A lot of 100 semiconductor chips contains 20 that are defective.
(a) Two are selected, at random, without replacement, from the lot. Determine the probability that the second chip
selected is defective.
(b) Three are selected, at random, without replacement, from the lot. Determine the probability that all are defective.
Let A and B denote the events that the first and second chips selected are defective, respectively.
2.6.7. Computer keyboard failures are due to faulty electrical connects (12%) or mechanical defects (88%). Mechanical
defects are related to loose keys (27%) or improper assembly (73%). Electrical connect defects are caused by defective
wires (35%), improper connections (13%), or poorly welded wires (52%).
(a) Find the probability that a failure is due to loose keys.
(b) Find the probability that a failure is due to improperly connected or poorly welded wires.
2.6.8. An article in the British Medical Journal [“Comparison of treatment of renal calculi by operative surgery, percutaneous
nephrolithotomy, and extracorporeal shock wave lithotripsy” (1986, Vol. 82, pp. 879–892)] provided the following
discussion of success rates in kidney stone removals. Open surgery had a success rate of 78% (273/350) and a newer
method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289/350). This newer method looked better,
but the results changed when stone diameter was considered. For stones with diameters less than 2 centimeters, 93%
(81/87) of cases of open surgery were successful compared with only 83% (234/270) of cases of PN. For stones greater
than or equal to 2 centimeters, the success rates were 73% (192/263) and 69% (55/80) for open surgery and PN,
respectively. Open surgery is better for both stone sizes, but less successful in total. In 1951, E. H. Simpson pointed out
this apparent contradiction (known as Simpson’s paradox), and the hazard still persists today. Explain how open
surgery can be better for both stone sizes but worse in total.