Michael has two laptops, Laptop X and Laptop Y. In any one year, the probabilityof Laptop X breaking down is 0.1 and the probability of Laptop Y breakingdown is 0.35. In any one year, what is the probability that(i) both laptops break down,(ii) Laptop X breaks down but Laptop Y does not,(iii) exactly one of the laptops breaks down?

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Answered: Michael has two laptops, Laptop X and…

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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For safety reasons, 3 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 3 systems detects theft with a probability of 0.85 independently of the others. es. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 3 systems will detect it. What is the probability that when a theft occurs, at least one of the 3 systems will detect it? Your answer should be rounded to 4 decimal places.
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A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?
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