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) = 0.34, P(A2) = 0.33, P(A3) = 0.43,
P(A1 ∪ A2) = 0.6, P(A1 ∪ A3) = 0.64,
P(A2 ∪ A3) = 0.67, P(A1 ∩ A2 ∩ A3) = 0.03

(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 or type 3 defect.

1 answer

0.25