In a certain factory, machines D, E and F all produce computer chips ofthe same type. Of their production, machines D, E and F, respectively produce 2%, 3%and 1% defective chips. Machine D produces 30% of the output of the factory, machineE 25% and machine F the rest.Suppose one chip is selected at random from the output of the factory and the chip isdefective(a) Use Bayes' theorem to find the probabilities that the chip was manufactured onmachines D, E and F.(b) Identify the data, hypotheses, likelihoods, prior probabilities and posterior proba-bilities.(c) Redo the computation of (a) using a Bayesian updating table.

Given that in a certain factory, machines D, E, and F all produce computer chips of the same type.…

Answered: In a certain factory, machines D, E and…

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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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(A,) = 0.15 P(A, U A2) = 0.17 P(A, U A3) = 0.15 P(A,) = 0.10 P(A,) = 0.08 P(A, U A) = 0.18 P(A, N Az nAz) = 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?
Eye color in humans is determined by a single pair of genes. If both genes are blue-eyed genes, then the person will have blue eyes; if they are both brown-eyed genes, then they will have brown eyes; and if one is a blue-eyed gene and the other is brown-eyed gene, then the person will have brown eyes. A baby receives one gene from each of its parents and the gene it receives is equally likely to be either of the two genes of that parent. Suppose that Mario and both of his parents have brown eyes, but that his sister has blue eyes. (a) What is the probability that Mario possesses a blue-eyed gene? (b) Suppose that Mario’s wife has blue eyes. What is the probability that a child of theirs will have blue eyes? (c) If their first child has brown eyes, what is the probability that their second child will also have brown eyes?
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.)
In a screw factor, there are two machines. Machine A and B that produce screws. Machine A produces 20% of the daily output, while machine B produces 80% of the daily output. Of their output, 10% and 2% of their output are defective, respectively. A box of 30 screws is chosen at random from a day's production and found one of them to be a. defective. What is the probability that this box came from machine A? A screw is chosen at random from a day's production and found to be defective. What is the probability that it came from machine A? b. C. What is the probability of defective product of this factory? th Quality assurance employee start testing a group of screws, what is the probability that the 4 screw will be defective?
In a screw factor, there are two machines. Machine A and B that produce screws. Machine A produces 10% of the daily output, while machine B produces 90% of the daily output. Of their output, 2% and 10% of their output are defective, respectively. A box of 30 screws is chosen at random from a day's production and found one of them to be а. defective. What is the probability that this box came from machine A? b. A screw is chosen at random from a day's production and found to be defective. What is the probability that it came from machine A? C. What is the probability of defective product of this factory? th Quality assurance employee start testing a group of screws, what is the probability that the 4 screw will be defective?
Three different machines M1, M2, and M3 are used to produce similar electronic components. Machines M1, M2, and M3 produce 20%, 30% and 50% of the components respectively. It is known that the probabilities that the machines produce defective components are 1% for M1, 2% for M2, and 3% for M3. If a component is selected randomly from a large batch, and that component is defective, find the probability that it was produced: (a) by M2, and (b) by M3.
A retailer of automobile parts has four employees, K, L, M, and N, who make mistakes in filling an order one time in 100, four times in 100, two times in 100, and six times in 100. Of all the orders filled, K , L, M, and N fill, respectively, 20%, 40%, 30%, and 10%. If a mistake is found in a particular order, what are the probabilities that it was filled by K, L, M, or N?
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.
Let S = {E1, E2, E3} be the sample space of an experiment and let A = {E1}, B = {E2}, and C = events from S. The probabilities of the sample points are assigned as follows: P(E,) = 0.35, P(E2) = 0.30, and P(E3) = 0.35. Find P(BC). {E2, E3} be Select one: O a. 0.65 O b. 0.70 O c. 0.35 O d. 0.30
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of .2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components areoperating. Assume that the components operate independently. Find the probability that;(a) Exactly two of the four components last longer than 1000 hours. (b) The subsystem operates longer than 1000 hours
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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