Question: 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

Source: S. W Hall, Analysis of Defectivity of Semiconductor Wafers by Contingency Table, Proceedings Institute of Environmental Sciences, Vol. 1 (1994), 177-183.

(a) Suppose you know that a wafer is bad. What then is the probability that it was produced from a die that had particles?

(b) Suppose you know that a wafer is good. What then is the probability that it was produced from a die that had particles?

(c) Are the two events, a good wafer and a die with no par­ticle, statistically independent? Explain.