2. Electrical circuit: An electrical connection consists of 6 components (see figure 1), which actindependently of each other. Let Ai be the event that component no. i works (i = 1, ..., 6), andassume that these have probabilities P (A1) = 0.5, P (A2) = 0.3, P (A3) = 0.4, P (A4) = 0.8, P (A5) = 0.6and P (A6) = 0.7.425•)•+36Figure 1: Connection of electrical components (blue line means wire)(a) We define B = A1 U A4. Explain in words what event B is. Calculate the probability of B, i.e. P (B).(b) Define C = (A5 n A6) U A3. Calculate P (C). Also, find the probability of current flowing in thecircuit.

Given that, There are 6 components in the circuit. They all work independently Ai be the event of…

Answered: 2. Electrical circuit : An electrical…

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 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.)
Q1A Hi wonderful Bartleby team, I need help with this exercise, please provide answer and short explanation for all the answers. Thanks in advance. The last part of it is the sentence and the options are: -(Reject/ Fail to reject) the null hypothesis. There (Is / Not) sufficient evidence to support the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment.
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?
A traveling salesman can be found at one of four cities (C1,C2,C3,C4) at any given time.His probability of being at these cities are P(C1) = 1/8, P(C2) = 1/8, P(C3) = 1/4, P(C4) =1/2. He always carries his cellphone with him. Let X be the event that his cellphone hascoverage. The conditional probabilities that his cell phone has coverage given what city heis at are as following: P(X|C1) = 1/2, P(X|C2) = 1, P(X|C3) = 3/4, P(X|C4) = 3/4.a. Given that today his cellphone has coverage, what is the probability that he is at city C2?b. Let Y be the event that his cellphone is at least 70% charged. He usually remembers torecharge his cell phone every evening so the probability that his cell phone is at least70% charged at any given time is 4/5. Events X and Y are independent. What is theprobability that his cellphone is less than 70% charged AND out of coverage at the sametime?
2) Events A and B have respective probabilities P(A) = 0.4 and P(B) = 0.5.You also know that P(A ∪ B) = 0.7.(a) What is P(A|B)?(b) What is P(B|A)?
How do you determine the following probabilities? 1.)For n=4 and π=0.11, what is P(X=0)? 2.)For n=11 and π=0.30, what is P(X=10)? 3.)For n=11 and π=0.50, what is P(X=9)? 4.)For n=2 and π=0.86, what is P(X=1)?
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…
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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