A maintenance firm has gathered the following information regarding the failure mechanism for air conditioningsystems.Gas LeaksYesNoEvidence ofYes5614electrical failure No2920If this is a representative sample of AC failure, find the following probabilities.(a) That there was a gas leak, given that there was evidence of electrical failure.(b) That there was evidence of electrical failure, given that there was a gas leak.(c) Let E be the event that there is a gas leak and let F be the event that there is evidence of electrical failure.Find P(E | FC).

Step 1:Given Evidence of electrical failure (yes)Evidence of electrical failure (no)Gas Leaks…

Answered: A maintenance firm has gathered the…

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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In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.† You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent eight shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of eight shark attacks.(b) What is the probability all eight shark attacks are nonfatal? (Round your answer to three decimal places.) (c) What is the probability that four or more of the eight shark attacks are nonfatal? (Round your answer to three decimal places.) (d) What is the expected number of nonfatal shark attacks out of the eight? What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
According to a recent study, 21% of patients who had been hospitalized for an acute myocardial infarction did not fill their cardiac medication by the seventh day of being discharged. Suppose there are twelve people who have been hospitalized for an acute myocardial infarction. (a) What are the number of trials n and the probability of "success" p in this case? n = 12✔ O , P = 0.21 0 Use technology to determine the following probabilities, rounding each to 4 decimal places. (b) Probability that all filled their cardiac medication. Answer = 0.0033 x (c) Six did not fill their cardiac medication. Answer = 0.2604 X (d) At most five did not fill their cardiac medication. Answer = 0.7546 x (e) None filled their cardiac medication. Answer = 0.000000 (f) At least five did not fill their cardiac medication. Answer = 0.4096 X (g) Suppose that five patients out of 12 who were discharged did not fill their medications. Is this unusual? Probability= 0.1868 X Because this probability is greater…
4.41 Legitimate probabilities? In each of the following situations, state whether or not the given assignment of probabilities to individual outcomes is legitimate—that is, satisfies the rules of probability. If not, give specific reasons for your answer. (a) When a coin is spun, P(H) 5 0.55 and P(T) 5 0.45. (b) When a coin flipped twice, P(HH) 5 0.4, P(HT) 5 0.4,
In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal.† You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent seven shark attacks, all of which were nonfatal. Let r be the number of nonfatal attacks out of a random sample of seven shark attacks. (b) What is the probability all seven shark attacks are nonfatal? (Round your answer to three decimal places.) (c) What is the probability that three or more of the seven shark attacks are nonfatal? (Round your answer to three decimal places.) (d) What is the expected number of nonfatal shark attacks out of the seven? What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
Samples of skin experiencing desquamation are analyzed for both moisture and melanin content. The results from 100 skin samples are as follows: Melanin Content High Low Moisture High 13 7 Content Low 48 32 Let A denote the event that a sample has high Melanin Content, and let B denote the event that a sample has low Moisture Content. Determine the following probabilities: P(A|B) and P(B|A). (Show complete solution in your answer sheet) a. 0.35, 0.1795 b. None among the choices c. 0.60, 079 d. 0.1795, 0.35
The following table gives joint probabilities as to whether an adult American male has high blood pressure and/or high cholesterol: Blood Pressure High OK .18 .22 Cholesterol High OK .15 .45 (a)What is the probability that an adult American male has both conditions? (b)What is the probability that an adult American male has high blood pressure? (c)What is the probability that an adult American male with high blood pressure also has high cholesterol? (d)Are “having high blood pressure" and "having high cholesterol" independent? Why?
A.2 According to Chemical Engineering Progress (November 1990), approximately 30% of all pipework failures in chemical plants are caused by operator error. (a) What is the probability that out of the next 20 pipework failures at least 10 are due to operator error?(b) What is the probability that no more than 4 out of 20 such failures are due to operator error?(c) Suppose, for a particular plant, that out of the random sample of 20 such failures, exactly 5 are due to operator error. Do you feel that the 30% figure stated above applies to this plant? Comment.
A diagnostic test for disease X correctly identifies the disease 95% of the time. False positives occur 12%. It is estimated that 0.18% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.) The percentage chance that the test will be positive = % The probability that, given a positive result, the person has disease X = %
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In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television-is there too much violence on television?" Use the data in the table to find the following probabilities, where Y is the event "saying yes," and M is the event "being a man." (Round the answers to two decimal places.)Yes No Don't Know TotalMen 162 95 23 280Women 256 45 19 320Total 418 140 42 600(a) p(Y' | M ) = (b) p(Y | M' ) = (c) p(Y' | M' ) = (d) Which event is the complement of the event Y|M?Y' | M'Y | M' Y' | M
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