Question: 26. A certain system can experience three different types of defects. Let Ai (i 1, 2, 3) denote the event that the system has

26. A certain system can experience three different types of defects. Let Ai (i 1, 2, 3) denote the event that the system has a defect of type i. Suppose that P(A1) .12 P(A2) .07 P(A3) .05 P(A1 A2) .13 P(A1 A3) .14 P(A2 A3) .10 P(A1 A2 A3) .01

a. What is the probability that the system does not have a type 1 defect?

b. What is the probability that the system has both type 1 and type 2 defects?

c. What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect?

d. What is the probability that the system has at most two of these defects?

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