A pavement can have three types of defect. Let Ai denote the event that the pave

Question

A pavement can have three types of defect. Let Ai denote the event that the pavement has cracking, A2 denote the event that pavement has rutting, and As denote the event that the pavement has potholes. Suppose: PlA1) = 0.12. P(Ag) = 0.07 , PAs) = 0.05, P(A1 UAg) = 0.13 , P(AgnAs) = 0.10 , P(A1 n A2 n As) = 0.01 What is the probability that the pavement does not have cracking? What is the probability that the pavement has both cracking and rutting? What is the probability that the system has at most two of these defects?

Explanation / Answer

1. Probability that the pavement does not have a cracking = P(A1)'

= 1 - P(A1) = 1 - 0.12 = 0.88.

2. Probability that the pavement has both cracking and rutting

= P(A1 A2)

= P(A1) + P(A2) - P(A1 U A2)

= 0.12 + 0.07 - 0.13

= 0.06.

3. Probability that the system has atmost two of these defects

= 1 - Probability that the system has all three defects

= 1 - P(A1 A2 A3)

= 1 - 0.01

= 0.99.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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