A yield improvement study at a semiconductor manufacturing f

A yield improvement study at a semiconductor manufacturing facility provided defect data for a sample of 450 wafers. The following table presents a summary of the responses to two questions: \"Was a particle found on the die that produced the wafer?\" and \"Is the wafer good or bad?\"

Quality of Wafer

Condition of Die

No Particles

Particles

Totals

Good

320

14

334

Bad

80

36

116

Totals

400

50

450

Referring to the above table, if a wafer is selected at random, what is the probability that :

a. it was produced from a die with no particles?

b. it is a bad wafer and was produced from a die with no particles?

c. it is a bad wafer or was produced from a die with particles?

d. Explain the difference in the results in (b) and (c).

Solution

a)

P(no particles) = 400/450 = 0.8888888889

b)

P(bad and no particles) = 80/450 = 0.177777778

c)

P(bad OR with particles) = (80 + 36 + 15)/450 = 0.291111111

d)

B used AND, that means, simultaneously, it has to be a bad wafer and no particles.

C used OR, that means, it suffices that EITHER it is a bad wafer OR with particles.