Question

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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” Were particles found on the die that produced the wafer?” and “is the wafer good or bad?”

CONDITION OF DIE
Quality of wafer	No particles	Particles	Totals
Good	320	14	334
Bad	80	36	116
Totals	400	50	450

1. Suppose you know that a wafer is bad. What then is the probability that it was produced from a die that had particles?
2. Suppose you know that a wafer is good. What then is the probability that it was produced from a die that had particles?
3. Are the two events, a good wafer and a die with no particles, statistically independent? Explain.

Show working

Answer 1

(a)

P(Particles/ Bad) = P(Particles AND Bad)/ P(Bad)

                    = 36/116

                    = 0.3103

So,

Answer is:

0.3103

(b)

P(Particles/ Good) = P(Particles AND Good)/ P(Good)

                    = 14/334

                    = 0.0419

So,

Answer is:

0.0419

(c)

P(Good) = 334/450 = 0.7422

P(No particles) = 400/450 = 0.8889

So,

P(Good) X P(No particles) = 0.7422 X 0.8889 = 0.6597

But

P(Good AND No particles) = 320/450 = 0.7111

Since P(Good) X P(No particles) = 0.6597 P(Good AND No particles) = 0.7111, the two events a good wafer and a die with no particles, are not statistically independent