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 type i. Suppose that

P(A₁) = 0.14, P(A₃) = 0.12, P(A₁ U A₃) = 0.2,

P(A₂ U A₃) = 0.18, P(A₂ \(\cap \) A₃) = 0.04, P(A₁ U A₂ U A₃) = 0.21.

(a) What is the probability that the system does not have a defect of type 1?

(b) What is the probability that the system has a type 1 defect but not a type 3 defect?

(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 a type 2 defect?

e) What is the probability that the system has at least one of these defects?

f) What is the probability that the system has none of these defects?