2. (Bayes formula, Ks) In the setup of an assembly line, the system is either correctly orincorrectly adjusted. The probability of a correct adjustment is 0.95. When correctly adjusted, thesystem operates with a 2% defective rate. However, if incorrectly adjusted, it has a 50%defective rate. Assume that defects occur independently of each other.(1) ( Complete the tree diagram below by filling in the relevant probabilities andconditional probabilities, where C (reşp., I) represents the event that the system is correctly(resp., incorrectly) adjusted, and D (résp., N) represents the event that the next produced item isdefective (resp., non-defective);(2) (r~-) After the system starts a production run, what is the probability that a defect isobserved?(Hint: D = (C N D) U (IND), Total Probability)(3), , Suppose that one item selected by an inspector is found to be defective. What is theprobability that the system is incorrectly adjusted? (Hint: P(I | D), Bayes Theorem)DItems produced whencorrectly adiustedDIIItems produced whenincorrectly adjusted

We will use given data and corresponding relation to find probability

Answered: 2. (Bayes formula, Ns) In the setup of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Under current economic circumstances, a stockbroker estimates that a client would invest in tax-free bonds (A) with a chance of 0.6 and in mutual funds (B) with a probability of 0.3. He has a 0.15 chance of investing in both tax-free and mutual funds. Determine the probability that the consumer will not invest in any of the two options at this moment.
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 5.6% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? c. What is the probability of not being awakened if the student uses three independent alarm clocks? d. Do the second and third alarm clocks result in greatly improved reliability? A. No, because the malfunction of both is equally or more likely than the malfunction of one. B. No, because total malfunction would still not be unlikely. C. Yes, because total malfunction would not be impossible, but it would be unlikely. D. Yes, because you can always be certain that at…
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (22)%, and (13)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2?
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A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2
A company buys microchips from three suppliers I, II and III. Supplier I has a record of providing microchips that contain 10% defective; supplier a defective rate of 5% and supplier III has a defective rate of 3%. Suppose 10%, 40% and 50% of the current supply came from suppliers I, II and III, respectively. If a randomly selected microchip is defective, what is the probability that it came from supplier II? Express your answer accurate to two decimal places. O 48 O..40 O something else O 44 O 41
A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are P(A) = P(B) = 0.95, P(C) = 0.91, and P(D) = 0.96. Find the probability that at least one of the four parts will work. Round to six decimal places.
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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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