A population of 500 semiconductor wafers contains wafers fro

A population of 500 semiconductor wafers contains wafers from 3 lots. The wafers are categorized by lot and whether they conform to a thickness specification. The following table presents the number of wafers in each category.

Conforming Nonconforming

Lot1 (78) (12)

Lot2 (125) (35)

Lot3 (210) (40)

Suppose that one of the wafers described above is selected at random. Let A denote the event that the wafer is from Lot 1 and let B denote the event that the wafer conforms to the thickness specification. Compute the following probabilities:

(a) P(A)

(b) P(B)

(c) P(AB)

(d) P(A U B)

(e) Are A and B independent events? Explain your answer.

Solution

a)

P(A) = (78+12)/500 = 0.18

b)

P(B) = (78 + 125 + 210) / 500 = 0.826

c)

P(A n B) = 78/500 = 0.156

d)

P(A U B) = (78+12+125+210)/500 = 0.85

e)

If A and B are independent, then P(A|B) = P(A).

As

P(A|B) = P(A n B)/P(B) = 0.156/0.826 = 0.188861985

and P(A) = 0.18,

as they are not equal, then they are NOT INDEPENDENT.