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) = 0.14 PIA2) = 0.10 P(A3) = 0.08P(A, U A2) = 0.16 PIA, U A3) = 0.18PIA2 U A3) = 0.14 PIA, NA2 N 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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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q5. An electronic assembly consists of two subsystems A and B. The following probabilities are known. P(A fails) = 0.25, P( A and B fail) = 0.14 and P(B fails alone) = 0.15. Evaluate (i) P (A fails alone) (ii) P (A fails given that B has failed) (Explain the solution using Venn diagram)
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) = 0.16 P(A2) = 0.10 P(A3) = 0.07 P(A₁ UA2) = 0.18 P(A2 UA3) = 0.14 P(A₁ UA3) = 0.18 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?
A machine produces defective parts with three different probabilities depending on its state of repair. If the machine is in good working order, it produces defective parts with the probability 0.02. If it's wearing down, it produces defective parts with probability 0.1. If it needs maintenance, a produces defective parts with probability 0.3. The probability that the machine is in good working order is 0.8. The probability that it needs maintenance is 0.1. Compute the probability that a randomly selected part will be defective.
A device can fail in four different ways with probabilities T1= 0.5, T2 = 0.1, T3 = 0.1, and 14 = 0.3. Suppose there are 10 devices that fail independently of one another. What is the probability of 3 failures of the first kind, 2 of the second, 1 of the third, and 4 of the fourth?
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Hamza comes to office located in Islamabad through different modes of transport. From his past data, itis known that the probability of him coming through car, bus, motorbike and rickshaw are respectively 3/10,1/5,1/10,2/5The probabilities that he will arrive to his office late are 1/4,1/3,1/12 if he comes bycar, bus and motorbike. Interestingly, he will not be late if he comes by rickshaw. Suppose, he arriveslate on Friday. What is the probability that he came by car?
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 the following probabilities are true. P(A1) = 0.10 P(A2) = 0.07 P(A3) = 0.06P(A1 ∪ A2) = 0.11 P(A1 ∪ A3) = 0.13P(A2 ∪ A3) = 0.11 P(A1 ∩ A2 ∩ A3) = 0.01 (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
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) = 0.09 P(A3) = = 0.07 P(A₁ U A₂) = 0.16 P(A₂ U A3) = 0.13 P(A₁ U A3) = 0.17 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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A congressional committee is composed of 10 members: 6 Republicans and 4 Democrats. On any given vote, members vote independently. Whereas Republicans always vote their party line, Democrats vote their party line with probability .8, and vote Republican with probability .2. On a rainy day only 3 committee members (selected w/o replacement) were present. Let X = number of Democrats present Y = Number who voted Democratic that day Display the table of joint probabilities fX,Y(i,j) for 0 ≤ j ≤ i, for i=0,1,2,3. We can say that p(i,j)=P[x=i, Y=j].

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