Urn A contains one red ball and four white balls and Um B contains three red balls and one white ball. Two balls are randomly drawn from Ur A and placed into Ur B,then two balls are randomly drawn from Urn B and returned to Urn A.a)Calculate the probability that both urns contain the same distribution of red and white balls after the draws as they did before the draws.b)The process described in the preamble to Question 3 is followed. Then, five balls are drawn from Urn B with replacement and the number of red balls drawn isnoted. If the number of red balls drawn is two, calculate is the probability that Urn B contains the same distribution of red and white balls as it did in the beginning?

a) Let's first determine the possible distributions of red and white balls in each urn. Urn A can…

Answered: Urn A contains one red ball and four…

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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n urn has 10 balls numbered 1, 2,...,10 and 3 are drawn with replacement.A gambler who gets 3 times 10 in his trial wins 200 USD.a) Find the start money that has to be paid to make this a fair game. b) Assume the start money is 3 dollar and on one day 1200 games are played.Find the expectation and the variance of the profit of the owner.c) Find the probability that the Casino looses money on a day with 1200 games..
2. In a particular class, 78% of the students have a smartphone, 38% have a smartphone and a tablet, and 3% have neither a smartphone nor a tablet. Find the probability that a randomly selected student has a; c)Smartphone but does not have a tablet a) Tablet ob)Tablet or a smartphone VITDA SluboM ov bmucqmoto yilidedon of SOS SLAoraimdue smstore srit stalgmos tesd liw tontbnow tiw nold srt wesitivitao bgan to bno etlu lo to toe
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An employment company has six men and 5 women who want to be assigned to a certain task. One employer wants to hire four employees as store clerks, and another employer wants to hire three employees as cleaners. Assuming each person has an equal chance of being hired at random and that only seven employees will be hired, fid the probability that: a) three men will be selected as cleaners b) three men will be selected as cleaners and four women will be selected as store clerks Sheka has a rare coin collection made up of 8 silver dollars, 7 quarters, and 5 dimes. She plans to sell 8 of the 20 coins to make some extra money. If she selects the coins at random, what is the probability that 3 silver dollars, 2 quarters, and 3 dimes are selected? A dog breeder has 15 puppies for sale. Eight are yellow Labs. If 5 puppies are selected at random, what is the probability that all ar yellow Labs?
1. A bag contains 12 gambling chips: 8 of these chips have a zero marked on them, the other 4 chips have a one marked on them. Another bag also contains 12 chips: 4 marked zero and 8 marked one. Players randomly select one chip from each bag and their score is the larger of the two numbers on the chips that they select. a) b) c) d) f) Present the probability distribution of the scores that could be achieved by a player in one game. Compute the mean (ux) and standard deviation (x) of this distribution. Present the sampling distribution of the total score that a player could achieve in three games, assuming chips are returned to their bags after each game. Present the sampling distribution of the mean score that could be achieved by a player in three games, assuming chips are returned to their bags after each game. Compute the mean (μ) and standard deviation (o) of the sampling distribution in part D. Confirm that u = μ that o =T. Vn What is the mean and standard deviation of the…
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6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.
Consider 3 urns. Ballot box A contains 3 white balls and 8 red balls, ballot box B contains 9 white balls and 8 red balls and ballot box C contains 10 white balls and 8 red balls. A ball is selected from ballot box 1 and placed in ballot box 2, then one is drawn from ballot box 2 and it is placed in ballot box 3, finally a ball is drawn from ballot box 3. What is the probability that the ball selected from ballot box 3 is white?

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