Question: 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

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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