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 type of i. Suppose that

P(A₁) = 0.12

P(A₂) = 0.07

P(A₃) = 0.05

P(A₁ A₂) = 0.13

P(A₁ A₃) = 0.14

P(A₂ A₃) = 0.10

P(A₁ A₂ A₃) = 0.01

a. What is the probability that the system does not have a type 1 defect?

b. What is the probability that the system has both type 1 and type 2 defects?

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 at most two of these defects?

Please show me vann diagram and all the necessary details and steps from scratch please. Thank you.