4.2 As part of the yield-improvement effort at a semicon- manufacturing facility

Question

4.2 As part of the yield-improvement effort at a semicon- manufacturing facility, a patterned wafer ection system was used to provide defect data for sample of 450 wafers. The results were cross- classified according to two characteristics: "was a on the die that produced the wafer?", particle found good or bad?" the wafer CONDITION OF DIE No Particles Particles Total Quality of Wafer 334 320 Good 36 116 Bad 400 500 Total (a) Give an example of a simple event (b) Give an example of a joint event. de) What is the complement of the event a good wafer? d) is a good wafer with no particles ajoint event? e) suppose that a wafer is selected at random. What is the probability that the wafer (1) is good? (2) has no particles? (3) is good or has no particles? is good and has no particles? (0 Suppose that the wafer selected has no particles. What then is the probability that it is good?

Explanation / Answer

Solution(a):

Simple event example is

No particle founds on the die that produced wafer = 400

Solution(b):

Joint Event example is

No particle found on the die that produced wafer and wafer is good = 320

Solution(c):

Complement of a good wafer is bad wafer

Solution(d):

A good wafer with no particle is joint event because there are two conditions in a single statement.

Solution(e):

Probability wafer is good = 334/550 = 0.74222

Probability with no particles = 400/450 = 0.888

Probability of good and no particles = 320 /450 = 0.7111

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