Q3. An automobile manufacturer is concerned about a possible recall of its best-

Question

Q3. An automobile manufacturer is concerned about a possible recall of its best-selling four-door sedan. If there was a recall, there is a probability of 0.25 of a defect in the brake system, 0.18 of a defect in the transmission system, 0.07 of a defect in both systems simultaneously, 0.17 of a defect in the fuel system, 0.22 of a defect in the lighting system, and 0.30 of a defect in some other area. (a) What is the probability that the defect is not in the brake system? (b) What is the probability that the defect is in the brake system or in the transmission system? c) What is the probability that there are no defects in either the brake or transmission system? (d) What is the probability that the defect is in the brake system but not in the transmission system? (e) What is the probability that the defect is in the fueling system or in some other area, if we know that (f) What is the probability that the defect is in the brake system, if the automobile has a defective in the (g) What is the probability that the defect is in the brake system, if the automobile does not have defective (h) Suppose that a fueling broken automobile has a defective in lighting system with probability 0.22, then (i) Are the two events in part (h) independent? these events are exclusive? transmission system? in the transmission system? what is the probability that a lighting broken automobile has a defective in fuel system?

Explanation / Answer

a) P(defect is not in brake system) = 1-0.25 = 0.75

b) P(defect in brake or transmission) = P(defect in brake) + P(defect in transmission) - P(defect in both)

= 0.25 + 0.18 - 0.07

= 0.36

c) No defects in either brake or transmission) = 1 - 0.36

= 0.64

d) P(defect in brake but not in transmission) = P(defect in brake) - P(defect in both)

= 0.25 - 0.07

= 0.18

e) P(defect in fueling system or in some other area) = 0.17 + 0.30

= 0.47

f) P(defect in brake | defect in transmission) = P(defect in both) / P(defect in transmission)

= 0.07/0.18

= 0.3889

g) P(defect in brake | no defect in transmission) = P(defect in brake but not in transmission) / P(defect in transmission)

= 0.18/(1-0.18)

= 0.2195

h) P(defect in lighting | defect in fuelling system) = 0.22

P(defect in lighting and fuelling) / P(defect in fuelling) = 0.22

P(defect in lighting and fuelling) = 0.22 x 0.17

P(defect in fuelling | defect in lighting) = 0.22 x 0.17 / P(defect in lighting)

= 0.22 x 0.17 / 0.22

= 0.17

i) P(defect in lighting and fuelling) = P(defect in lighting) x P(defect in fuelling)

So, the events are independent

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

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