A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A₁) = 0.15 P(A₂) = 0.11 P(A₁ U A₂) = 0.18 P(A₁ U A3) P(A₂ U A3) = 0.14 P(A₁ A₂ A3) = 0.02 (a) What is the probability that the system does not have a type 1 defect? P(A3) = 0.07 = 0.18 (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?

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A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect
of type i. Suppose that the following probabilities are true.
P(A₁) = 0.15
P(A₂) = 0.11 P(A3) = 0.07
P(A₁ U A3) = 0.18
P(A₁ U A₂) = 0.18
P(A₂ U A3) = 0.14
P(A₁ A₂ A3) = 0.02
(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?
Transcribed Image Text:A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A₁) = 0.15 P(A₂) = 0.11 P(A3) = 0.07 P(A₁ U A3) = 0.18 P(A₁ U A₂) = 0.18 P(A₂ U A3) = 0.14 P(A₁ A₂ A3) = 0.02 (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?
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Since you have posted a question with multiple subparts, we will solve first three subparts for you. To get remaining subparts solved, please repost the question and mention the subparts to be solved. 

Probability is the likelihood or chance of event happening. It takes the value between 0 to 1. The union of two events is calculated using the formula :

PA1A2=PA1+PA2-PA1A2

Here, PA1A2 is intersection of two events. Probability is calculated by dividing the favorable number of events and the total number of events. 

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