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.= 0.10P(A₁) =P(A₁ U A₂) = 0.11P(A₂) = = 0.07P(A3)= = 0.05P(A₁ UA3) = 0.12P(A₂ U A3) = 0.10P(A₁ A₂ A3) = 0.01n(a) Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (Round your answer to four decimal places.)0.0601 X(b) Given that the system has a type 1 defect, what is the probability that it has all three types of defects? (Round your answer to four decimal places.)(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.)

here as per guidelines i have calculated 3 subparts kindly repost for remaining HERE FROM GIVEN…

Answered: (a) Given that the system has a type 1…

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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A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large. The survey found that 65% of the respondents do believe inequality is too large. In a sample of six British citizens, what is the probability that two believe inequality is too large? If required, round your answer to four decimal places.f (2) = In a sample of six British citizens, what is the probability that at least two respondents believe that inequality is too large? If required, round your interim calculations and final answer to four decimal places.P (at least 2) = In a sample of four British citizens, what is the probability that none believe inequality is too large? If required, round your answer to four decimal places.f (0) =
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 2.5 accidents per 100,000 flight operations. (b) Find the probability of no accidents in 100,000 flight operations. (Use 4 decimal places.)(c) Find the probability of at least 8 accidents in 200,000 flight operations. (Use 4 decimal places.)
(a) Student A would like to visit a country where 92% of the population speaks the native language. However, Student A does not speak and understand that language. What is the probability that at least two of three locals at the immigrant department of the airport will succeed to communicate with Student A? Answer = Answer (b) Research Scientist A investigates the infected laboratory rats in modeling human diseases. Research Scientist A finds out the probability of the laboratory rats getting infected is two out of ten. What is the probability that five laboratory rats must be required before Research Scientist A finds at least three laboratory rats but not all have been infected? Answer = Answer (c) A badminton game consists of at least two matches, and each match consists of 21 points. The probability of Player A and Player B earning a point in their matches are 80% and 90%. What is the probability difference between Player A and Player B to get their second points within…
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In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D) = 0.750, where D is directly in person. If someone is randomly selected, what does P (D) represent, and what is its value? What does P (D represent? O A. P(D) is the probability of randomly selecting someone who did not participate in the survey. B. P(D) is the probability of randomly selecting someone who chooses a direct in-person encounter as the most fun way to flirt. C. P(D) is the probability of randomly selecting someone who did not have a preference in regards to the most fun way to flirt. D. P(D) is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt.
Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?
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Q. 2 The probability that a smoker who consumes over 20 cigarettes a day will suffer from chronic respiratory illness is 4 The 10 probability that he will suffer from heart disease is The 10 probability that he will suffer from at least one of these ailments is 6.5 10 (i) Find the probability that the smoker will suffer from both ailments. (ii) Find the probability that he will suffer from heart disease given that he suffers from chronic respiratory illness. (iii) Find the probability that he will suffer from chronic respiratory illness given that he suffers from heart disease. (iv) Are events "chronic respiratory illness" and "heart disease independent"?
Charlie is about to take two laps in the school swimming pool. The time of his first lap is X minutes, where X is an Exponential(1) random variable. The time of his second lap is Y minutes, where Y is an Exponential(X) random variable. What is the probability that he completes his second lap within one minute?
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