Question

The data in the table represents the breakdown of semiconductor wafers by lot and whether they conform to a thickness specification. If one wafer is selected at random, a) what is the probability that the wafer conforms to specifications? b) what is the probability that the wafer is from Lot A and conforms to specifications? c) what is the probability that the wafer is from Lot A or conforms to specifications? d) what is the probability that the wafer conforms to specifications, given the wafer is from Lot A? e) Are the events “from Lot A” and “conforms to specifications” independent? Why or why not? Use the results from some of the previous parts of this exercise to answer part e.

Lots	Conforms to specifications	Does not conform to specifications	Totals
A	88	12	100
B	171	29	200
C	254	46	300
Totals	513	87	600

Answer 1

a)

Out of 600 wafers, 513 conforms specification so  the probability that the wafer conforms to specifications is

P(conforms to specification) = 513 / 600 = 0.855

b)

The probability that the wafer is from Lot A and conforms to specifications is

P(Lot A and conforms specification) = 88 / 600 = 0.1467

c)

The probability that the wafer is from Lot A or conforms to specifications is

P(Lot A or conforms specification)=P(Lot A)+P(conforms specification)-P(Lot A and conforms specification) = 100/600 + 513/600 - 88/600 = 0.875

d)

Out of 100 wafers of lot A, 88 conforms specification so the probability that the wafer conforms to specifications, given the wafer is from Lot A is

P(Conforms specification | lot A) = 88 / 100 = 0.88

e)

Since P(Conforms specification | lot A)is not equal to P(conforms to specification) so the events “from Lot A” and “conforms to specifications” are independent.