Of nine executives in a business firm, four are married, three have never married, and two are divorced. Three of the executives are to be selected for promotion. Let Y, denote the number of marriedexecutives and Y, denote the number of never-married executives among the three selected for promotion. Assuming that the three are randomly selected from the nine available, find the joint probabilityfunction of Y, and Y2-Y1y22.3

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Answered: Of nine executives in a business firm,…

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 person died prematurely, find the probability with which he could have been a heavy smoker given the following data: Off all people: 50% of people don't smoke, 20% are light smokers & 30% are heavy smokers. Heavy smokers are twice as likely to die prematurely as light smokers, light (6 marks) smokers are twice as likely to die prematurely as nonsmokers.
Suppose a committee of 3 people is going to be formed from faculty that consists of 30 professors and 14 lecturers. Find the probability of randomly selecting at least one lecturer to be part of the committee, assuming assuming this is without replacement. a. 0.683 b. 0.973 c. 0.693 d. 0.968
Suppose that 2 defective microwaves have been included in a shipment of 6 microwaves. The buyers want to test the 6 microwaves one at a time. Let Y denote the number of defective microwaves is found after 3 random selected ones have been tested. a. Calculate the probability that the buyers can find at least 1 defective microwave after 3 have been tested? b. Find the probability that buyers cannot find any defective microwave after 3 random ones have been tested?
Two boxes each contain long and short bolts. Box 1 contains 60 long and 40 short bolts, while box 2 contains 10 long and 20 short bolts. One box is selected at random and one bolt is then chosen from the selected box. a. Find the probability the chosen bolt is long. b. Given that the chosen bolt was long, find the probability that box 1 was selected.
Of the cartons produced by a company, 5% have a puncture, 6% have a smashed comer, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed comer. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.) %.
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In a pastry shop in a small town, the probability that a customer buys apple tarts is0.45, the probability they buy an apple pie is 0.69 and the probability that they buy bothan apple tart and an apple pie is 0.27. A customer is chosen at random.i. Find the probability that they buy an apple tart or an apple pie. ii. Given that a customer buys an apple pie, what is the probability that they alsobuy an apple tart? b) The weight of a green forest frog has a normal distribution with mean 150.3 g and astandard deviation of 5g. Find the probability that a randomly selected frog weighsi. Less than 153g ii. Between 150 g and 158 g c) The random variable X is normally distributed such that X~N(?, 12). It is known that?(? > 32) = 0.0618. find the value of ?.
Suppose that 80% of American homes have a microwave oven. Let X be the number of American homes in a random sample of n=20 that have a microwave oven. Find the probability that X is at most 18 and at least 16.
There are two boxes. Box A contains 6 red balls, and 4 blue balls andBox B contains 4 red balls and 8 blue balls. A die is rolled, if the number is lessthan 3, a ball is selected from box A. If the result is 3 or more, a ball is selectedfrom Box B. Calculate:a. The probability that the ball will be red and selected from Box B.b. The probability that the ball will be blue.
Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.
A platter contains 48 doughnuts: 26 cake, 13 glazed, and nine jelly-filled. Suppose two doughnuts are randomly selected in succession without replacement. Find the probability (to 4 decimal places) of selecting two cake doughnuts. A. 0.0691 B. 0.2881 C. 0.2934 D. 0.5417
Q10. Given that the switchboard of a consultant's office receives on average 0.8 calls per minute, find the probability that in a 5-minute interval there will be exactly 4 calls, and in the following 4- minute interval, there will be exactly 1 call. (Consider the entire 9 minute interval to calculate your answer.)

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