A certain system can experience three different types of defects. Let A_i (i = 1

Question

A certain system can experience three different types of defects. Let A_i (i = 1, 2, 3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A_1) = 0.15 P(A_2) = 0.10 P(A_3) = 0.07 P(A1 Union A_2) = 0.18 P(A_1 Union A_3) = 0.18 P(A_2 Union A_3) = 0.14 P(A_1 Intersection A_2 Intersection A_3) = 0.01 (a) What is the probability that the system does not have a type 1 defect? (No Response) (b) What is the probability that the system has both type 1 and type 2 defects? (No Response) (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (No Response) (d) What is the probability that the system has at most two of these defects? (No Response)

Explanation / Answer

a)probability =1-P(A1)=1-0.15=0.85

b) probability=P(A1nA2)=P(A1)+P(A2)-P(A1nA2)=0.15+0.10-0.18=0.07

c) Probability =P(A1nA2)-P(A1nA2nA3)=0.07-0.01=0.06

d)probability =1-P(A1nA2nA3)=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.