Problem #7: 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
P(A_(1))=0.28,P(A_(2))=0.33,P(A_(3))=0.36 P(A_(1)\cup A_(2))=0.54,P(A_(1)\cup A_(3))=0.55 P(A_(2)\cup A_(3))=0.6,P(A_(1)\cap A_(2)\cap A_(3))=0.04
(a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type 2 defect and does not have a type 3 defect.

Question

Problem #7: 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

P(A_(1))=0.28,P(A_(2))=0.33,P(A_(3))=0.36
P(A_(1)\cup A_(2))=0.54,P(A_(1)\cup A_(3))=0.55
P(A_(2)\cup A_(3))=0.6,P(A_(1)\cap A_(2)\cap A_(3))=0.04

(a) Find the probability that the system has exactly 2 of the 3 types of defects. (b) Find the probability that the system has a type 1 defect given that it does not have a type 2 defect and does not have a type 3 defect.

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Expert Answer to - Problem #7: A certain system can experience three different types of defects. Let A_(i)(i)=(1,2,3) d

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Solution for - Problem #7: A certain system can experience three different types of defects. Let A_(i)(i)=(1,2,3) d

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(Solved): Problem #7: A certain system can experience three different types of defects. Let A_(i)(i)=(1,2,3) d ...

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