Your company is considering offering 600 employees the opportunity to transfer to its new headquarters in Ottawa and, aspersonnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that yourcompany currently employs 300 managers, 400 factory workers, and 300 miscellaneous staff, find the following probabilities,leaving the answers as formulas.(a) All the managers will be offered the opportunity.(b) You will be offered the opportunity.88

There are 300 managers, 400 factory workers and 300 miscellaneous staff. Total number of employees =…

Answered: Your company is considering offering…

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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the carnival has come to town, and lucky louie has once again set up his pavilion. He offers a simple game consisting of rolling two normal six-sided dice at the same time for the extraordinarily low price of $3.00 per play. If the player rolls a sum of 3, the player wins $13.00; if the sum is a 9, the player wins $9.00; and if the sum is a 12, the player wins $12.00. Otherwise, the player does not win anything. How much should you expect to win or lose per game (after paying the $3.00) ?
Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
A large retail lawn care dealer currently provides a 2-year warranty on all lawn mowers sold at its stores. A new employee suggested that the dealer could save money by just not offering the warranty. To evaluate this suggestion, the dealer randomly decides whether or not to offer the warranty to the next 50 customers who enter the store and express an interest in purchasing a lawnmower. Out of the 25 customers offered the warranty, 10 purchased a mower as compared to 4 of 25 not offered the warranty. a. Place a 95% confidence interval on 7₁ - 72, the difference in the proportions of customers purchasing lawnmowers with and without the warranty. b. Test the research hypothesis that offering the warranty will increase the propor- tion of customers who will purchase a mower. Use a = .05. c. Are the conditions for using a large-sample test to answer the question in part (b) satisfied? If not, apply an exact procedure,
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…
A vending machine contains 1000 lollipops. Some of the lollipops are red, and the others are blue. You don’t know how many there are of each color. However, you do know that these two alternatives are equally likely. There are 900 blue lollipops and 100 red ones. There are 500 blue lollipops and 500 red ones. When you put a coin into the vending machine, it gives you a lollipop, chosen at random. Suppose that it gives you a blue lollipop. What is the probability that there are 900 blue lollipops and 100 red ones? Show how you got the answer.
A construction company submitted a bid for a large, public construction project. The company’s management initially felt they had a 50-50 chance of getting the project. However, the department to which the bid was submitted subsequently requested additional information on the bid submitted by this company. Past experience indicates that for 75% of the successful bids but only for 40% of the unsuccessful bids the agency requested such additional information. Question: Given that the construction company was asked for additional information, what is the probability that it will get the project?
In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week. Each bet is classified according to two variables: result of picking the Crush ("Crush won" or "Crush lost") and bet placed the following week ("Picked Crush to win" or "Picked Crush to lose"). In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent. Round your answers to two…
In an experimental study, researchers had each of their participants bet on each game of a professional football season. In the contingency table below is some information from a random sample of 100 bets from this study placed on the Columbus Crush (picking them to win) during the last 14 games of the season (the Crush had 7 wins and 7 losses over that period). The table indicates, for each bet placed on the Crush, whether or not the team won and how the participant who placed the bet wagered the following week. Each bet is classified according to two variables: result of picking the Crush ("Crush won" or "Crush lost") and bet placed the following week ("Picked Crush to win" or "Picked Crush to lose"). In the cells of the table are the respective observed frequencies, and three of the cells also have blanks. Fill in these blanks with the frequencies expected if the two variables, result of picking the Crush and bet placed the following week, are independent. Round your answers to two…
A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers(red), as well as 0 and 00 (which are green). You bet 5 dollars that the outcome is anodd number. If you win you get 10 dollars; otherwise you lose your 5 dollars. Note:assume the 0 and 00 numbers are considered even numbers What is your expected winnings? Which of these options is best: bet on an odd number or don’t bet? Why?
A father and his three children decide to hold a vote to select an after dinner activity. They will either see a play or a movie. If the majority of the family agrees on a preferred activity, then they will do that activity. If two family members vote to see a play and the other two family members vote to watch a movie, then (since the father will pay for the activity), the father's vote will be used to break the tie. (a) How many winning coalitions are there in this situation? (b) Find one of the children's Banzhaf power index.

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