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
the following probabilities are true.

P(A₁) =
0.10      P(A₂)
=
0.07     P(A₃)
= 0.05
P(A₁ U A₂) =
0.11      P(A₁
U A₃) = 0.12
P(A₂ U A₃) =
0.10      P(A₁
n A₂ n A₃) = 0.01

(b) Given that the system has a type 1 defect, what is the
probability that it has all three types of defects? (Round your
answer to four decimal places.)

(c) Given that the system has at least one type of defect, what
is the probability that it has exactly one type of defect? (Round
your answer to four decimal places.)

(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? (Round your answer to four decimal places.)