Answer:
The probability that an item selected for inspection is classified as defective is 0.01485.
Step-by-step explanation:
Denote the events as follows:
A₁ = an item produced by the company is defective.
A₂ = an item produced by the company is not defective.
X = an item is classified as defective by the inspector.
Given:
P (X|A₁) = 0.99
P (X|A₂) = 0.005
P (A₁) = 0.01
P (A₂) = 1 - P (A₁) = 1 - 0.01 = 0.99
The law of total probability states that:
[tex]P(B)=P(B|A)P(A)+P(B|C)P(C)[/tex]
Use this law to compute the probability that an item selected for inspection is classified as defective as follows:
[tex]P(X)=P(X|A_{1})P(A_{1})+P(X|A_{2})P(A_{2})\\=(0.99\times0.01)+(0.005\times0.99))\\=0.01485[/tex]
Thus, the probability that an item selected for inspection is classified as defective is 0.01485.
