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) = 0.12

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