12-30. The probability that a contractor will get a plumbing contract is 2/3, and theprobability that he will not get an electric contract is 5/9. If the probability of getting at least one controis 4/5, what is the probability that he will get both the contracts?

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Answered: 12:30. The probability that a…

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 poker player has either good luck or bad luck each time she plays poker. She notices that if she has good luck one time, then she has good luck the next time with probability 0.2 and if she has bad luck one time, then she has good luck the next time with probability 0.4. What fraction of the time in the long run does the poker player have good luck?
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Frank noticed that his mother will serve salad with dinner 78% of the nights, will serve potatoes with dinner 30% of the nights and will serve both 14% of the nights. The probability, to the nearest hundredth, that Frank's mother will serve salad or potatoes is
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"?
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Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.
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Q1. Some couples planning a new family would prefer at least one child of each sex. The probability that a couple’s first child is a boy is 0.512. In the absence of technological intervention, the probability that their second child is a boy is independent of the sex of their first child, and so remains 0.512. Imagine that you are helping a new couple with their planning. If the couple plans to have only two children: What is the probability that at least one girl is born?
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12:30. The probability that a contractor will get a plumbing contract is 2/3, and the probability that he will not get an electric contract is 5/9. If the probability of getting at least one contro is 4/5, what is the probability that he will get both the contracts?