A strand of patio lanterns has 10 identicallights. If one light in the strand fails towork, the entire strand of lights will notwork. In order to have a 90% probabilitythat the entire strand of lights will work,what is the maximum probability of failurefor each individual light?

A strand of patio lanterns has 10 identical lights. If one light in the strand fails to work, the…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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You are the manager of a manufacturing plant and you are responsible for quality control. Each day, a random sample of 10 items is selected from the production line and tested by a quality control technician. A item can be in good condition or defective, and the probability that an item is defective is 0.05. You know by experience that the technician records the result of the test on an item correctly 80% of the time. Let X be the number of items that were recorded as defective by the technician (in the sample of 10 tested items). (a) Find the probability P(X= 1). (b) If the technician recorded one defective item in the sample, what is the conditional probability that there was no defective item in the sample?
To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,400, and the commission for each new account opened is $4,900. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account. Determine the equation for computing Gustin's profit per seminar, given static values of the relevant parameters. Profit =(New accounts opened x _______)-_________ Construct a simulation model to analyze the profitability of Gustin's seminars. Would you recommend that Gustin continue running the seminars? (Use at least 1,000 trials. Round your answer to two decimal places.) What is the minimum number of attendees (in a multiple of five, i.e., 25, 30, 35, …) that Gustin needs before a seminar's average profit is greater than zero? =______ attendees
A poll found that 15% of adults do not work at all while on summer vacation. In a random sample of 8 adults, let x represent the number who do not work during summer vacation. Complete parts a through e.
Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 27% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of &5 freshmen is selected. Round the answer to at least four decimal places. Part: 0 / 6 Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline? It is v appropriate to use the normal curve, since np = v 10 and n (1 – p) = 1 V 10. Part: 1 / 6 Part 2 of 6 Find the probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline. The probability that less than 32% of the freshmen in the sample are planning to major in a STEM discipline is|1. Part 3 of 6 A new sample of 130 freshmen is selected. Find the probability that less than 29% of the freshmen in this new sample…
You roll a fair die twice. What is the probability that the minimum of the 2 rolls is greater than 3 given that the sum of the two rolls is odd.
Professor Brown gives her students a maximum of three attempts to pass a final examination in her statistics course. She has found that the probability of passing on the first attempt is 0.40, the probability of passing the second attempt is 0.65 and the probability of not passing the third attempt is 0.15. Find the probability that a randomly selected student of hers will pass the final examination
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The three-year recidivism rate of parolees in a certain state is about 20%; that is, 20% of parolees end up back in prison within three years. Assume that whether one parolee returns to prison is independent of whether any of the others return. Complete parts a and b below. Find the probability that exactly 6 out of 20 parolees will end up back in prison within three years. The probability that exactly 6 out of 20 parolees will end up back in prison is nothing.
It is equally probable that two signals reach a receiver at any instant of the time T. The receiver will be jammed if the time difference in the reception of the two signals is less than T. Find the probability that the receiver will be jammed.
The device consists of 3 elements. The probability of failure free operation of each of them are respectively equal to. 0.6, 0.7, 0.8. Find the probability that at least two of elements will work without fail.
The height of male students in the school is assumed to be normally distributed. 18% of the students haveheight more than 180 cm and 9% of them have height less than 160 cm. Find µ and σ.
Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.

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what is the maximum probability of failure for each individual light?