The QMplus-gremlins are mischievous creatures that cause computer problems. After careful research you observe that the number ofgremlins active each day is a random variable with Bin(3, 0.5) distribution. If no gremlins are active, the probability of QMplus failureis 0.15; if one gremlin is active the probability of QMplus failure is 0.3; if two or more gremlins are active the probability of QMplusfailure is 0.5. You conclude that the total probability of QMplus failure on a given day is(to two decimal places). Assumingthere is a failure, the probability no gremlins are active is(again to two decimal places).

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Answered: The QMplus-gremlins are mischievous…

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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As a warehouse manager, it is your responsibility to inspect a large shipment of components for defects. Two independent random samples, each of size 20 of these components will be checked, and the shipment will be accepted if fewer than 3 of these components are defective in both samples. What is the probability of accepting a shipment containing 10% defectives?
If a seed is planted, it has a 95% chance of growing into a healthy plant.If eleven seeds are planted, what is the probability that exactly three don't grow?
A boxcar contains 6 complete car systems. 2/6 are randomly selected for tested and then classified as defective or not defective. If 2/6 are defective, find the probability that at least one of the systems will be defective.
If a seed is planted, it has an 80% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 1 doesn’t grow?
It has been found from experience that there is an average of five faults per 50 metres of cloth produced by a linen factory. If we randomly select 50 metres of cloth, what is the probability that there will be more than two faults?
A letter is taken at random out of "ASSISTANT" and out of "STATISTICS". What is the chance that they are the same letters?
Your son is a teacher in a state university. As per her class rule, the probability of not getting an additional points for a major examination is 2/3. If there are three engineering students to be selected at random, evaluate the probability that at least one of them gets additional points.
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected (a) next week and (b) in 3 weeks?
Students in a psychology class are identified as either introverts or extroverts using a personality quiz. They are then asked how many close friends they have. The results are summarized in the table. Data fewer than 5 close friends 5 or more close friends introvert 15 3 extrovert 11 21 1. What is the probability that one of the students selected at random is an introvert with fewer than 5 close friends? 2. What is the probability that one of the students selected at random is an extrovert? 3. What is the probability that one of the students selected at random has fewer than 5 close friends?
In a specific type of electronic card, the probability of a transistor being defective is 0.01. Let's assume there are 200 transistors on the electronic card. If there are no defective transistors, the electronic card is considered to be functioning. What is the probability of any electronic card not functioning?
A pharmaceutical company is running trials on a new test for anabolic steroids. The company uses the test on 400 athletes known to be using steroids and 200 athletes known not to be using steroids. Of those using steroids, the new test is positive for 375 and negative for 25. Of those not using steroids, the test is positive for 25 and negative for 175. What is the relative frequency of a false negative result (the probability that an athlete using steroids will test negative)? (Round your answer to two decimal places.) What is the relative frequency of a false positive result (the probability that an athlete not using steroids will test positive)? (Round your answer to two decimal places.)

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