9. (Ch. 2.2) A company produces a certain product, and each unit of this product
ID: 3351078 • Letter: 9
Question
9. (Ch. 2.2) A company produces a certain product, and each unit of this product may have 3 different types of defects. Let D D2,Ds represent the three different kinds of defects. Suppose further that for each unit produced P(D) = .12 PDs) = .05 PlDi U D) = .14 P(D2) = .07 PlDoU Ds) = .1 (a) What is the probability that a unit does not have a type 1 defect? (b) What is the probability that a unit has both a type 2 and 3 defect? (c) What is the probability that a unit has both a type 2 and 3 defect, but not a type 1 defect? (d) What is the probability that a unit has at most two defects?Explanation / Answer
as P(AnB)=P(A)+P(B)-P(AUB)
hence P(D1nD2)=P(D1)+P(D2)-P(D1UD2)=0.12+0.07-0.13=0.06
P(D1nD3)=P(D1)+P(D3)-P(D1UD3)=0.12+0.05-0.14=0.03
P(D2nD3)=P(D2)+P(D3)-P(D2UD3)=0.07+0.05-0.1=0.02
a)
probability =1-P(D1)=1-0.12=0.88
b) probability=P(D2nD3) =0.02
c)probability=P(D2nD3)-P(D1nD2nD3) =0.02-0.01 =0.01
d)probability=P(D1)+P(D2)+P(D3)-P(D1UD2)-P(D1UD3)-P(D2UD3) =0.12+0.07+0.05-0.06-0.03-0.02=0.13
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.