= .13 = .14 O=.10 n A3) = .01 at the system has a type 1 defect, what is the probability that it has a type 2 at the system has a type 1 defect, what is the probability that it has all three e at the system has at least one type of defect, what is the probability that it e type of defect? at the system has both of the first two types of defects, what is the probab have the third type of defect?

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How can I answer the letters b, c, and d? 

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 U A2) = .13
P(A1 U A3) = 14
P(A2 U A3) = 10
P(A1n A2 n A3) = .01
a. Given that the system has a type 1 defect, what is the probability that it has a type 2
defect?
b. Given that the system has a type 1 defect, what is the probability that it has all three types
of defects?
c. Given that the system has at least one type of defect, what is the probability that it has
exactly one type of defect?
d. Given that the system has both of the first two types of defects, what is the probability that
it does not have the third type of defect?
Transcribed Image Text: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 U A2) = .13 P(A1 U A3) = 14 P(A2 U A3) = 10 P(A1n A2 n A3) = .01 a. Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? b. Given that the system has a type 1 defect, what is the probability that it has all three types of defects? c. Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? d. Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect?
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