Suppose that 1 out of every 5,000 pieces of checked luggage contains a dangerous

Question

Suppose that 1 out of every 5,000 pieces of checked luggage contains a dangerous proscribed substance. A luggage screening machine has a false positive rate of 0.4% and a false negative rate of 0.03%.

(a) A piece of dangerous luggage is screened. What is the probability that the machine gives a positive reading?

(b) A piece of luggage is screened and the machine gives a positive reading. What is the probability that the luggage is dangerous?

(c) A piece of luggage is screened and the machine gives a positive reading. What is the probability that the luggage is safe?

(d) A piece of luggage is screened and the machine gives a negative reading. What is the probability that the luggage is safe?

(e) A piece of luggage is screened and the machine gives a negative reading. What is the probability that the luggage is dangerous?

Explanation / Answer

FP = 0.004

TN=0.996

TP=0.9997

FN=0.0003

a) Probability that mahine gives a positive reading = TP=0.9997

b) Probability = [0.9997]/[0.9997+0.004]=0.9961

c) Probability = 0.0039

d) P= 0.996/[0.996+0.0003]=9960/9963

e) P= 1- 9960/9963=3/9963

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.