A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote...

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(A₁) = 0.29, P(A₂) = 0.27, P(A₃) = 0.36,
P(A₁ ∪ A₂) = 0.52, P(A₁ ∪ A₃) = 0.57,
P(A₂ ∪ A₃) = 0.58, P(A₁ ∩ A₂ ∩ A₃) = 0.01

(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.

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orchestra answered 1 year ago

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