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.
