There are two boxes. At first, each box contains one white ball and one black ball. At each step, we drawone ball from each box randomly and exchange them. If we set thatState 1 = Box 1 contains no white balls,State 2= Box 1 contains one white ball,State 3 = Box 1 contains two white balls.1. Find the transition matrix.Answer:2. After 10 steps, what is the probability that box 1 contains two white balls?Answer:Submit Question

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Answered: There are two boxes. At first, each box…

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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Sally and Mike are playing frisbee at the beach. When Sally throws the frisbee the probability is 0.13 that it comes back to Sally, the probability is 0.7 that it goes to Mike, and the probability is 0.17 that the dog runs away with the frisbee. When Mike throws the frisbee there is a 0.62 probability that Sally gets it, a 0.27 probability that it comes back to Mike, and a 0.11 probability that the dog runs away with the frisbee. Treat this as a 3--state Markov Chain with the dog being an absorbing state. (a) If Mike has the frisbee, what is the expected value for the number of times the frisbee will be thrown before the dog gets the frisbee and runs away with it? (Give your answer correct to 2 decimal places.) times thrown (b) If Mike has the frisbee, what is the expected value for the number of times Mike will throw the frisbee before the dog gets it? (Give your answer correct to 2 decimal places.) times Mike throws
Consider an M/M/1 queueing system. Find the probability of finding at least n customers in the system.
José plays basketball. He makes free throw shots 43% of the time. José must now attempt two free throws. The probability that José makes the second free throw given that he made the first is 0.49. Is José's first free throw shot independent of his second free throw shot? There is not enough information to determine whether or not the two free throws are independent of each other. The two free throws are dependent on each other. O The two free throws are independent of each other. What is the probability that José makes both free throws? Round your answer to three decimal places.
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
In a town, there are three bridges: Bridge A, Bridge B, and Bridge C. On any given day, the probability of each bridge being open for passage is as follows: P(A) = 0.4, P(B) = 0.3, and P(C) = 0.5. If a resident needs to cross all three bridges in succession, what is the probability of successfully crossing all three bridges without encountering any closures?
The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: G
Your probability professor has a tabby cat who sleeps 34% of the time and seems to respond to stimuli more or less randomly. If a human pets her when she’s awake, she will request more petting 8% of the time, food 38% of the time, and a game of fetch the rest of the time. If a human pets her when she’s asleep, she will request more petting 33% of the time, food 41% of the time, and a game of fetch the rest of the time. (You can assume that the humans don’t pet her disproportionally often when she’s awake.) • If the cat requests food when petted, what is the probability that she was asleep? • If the cat requests a game of fetch when petted, what is the probability that she was not asleep?
Q4. A shipment of two boxes, each containing eight telephones, is received by a store. Box 1 contains two defective phones and box 2 contains one defective phone. After the boxes are unpacked, and all phones are mixed. Then a phone is selected and that was found to be defective. Find the probability that it came from box 2.
A system has five components connected as shown in the diagram. Assume A, B, C, D, and E function independently. If the probabilities that A, B, C, D, and E function 0.50, 0.65, 0.75, 0.95, and 0.80 respectively, what is the probability that the system fails?
Megan has a l100-song playlist on her phone that consists of 25 country songs, 50 rock songs, and 25 rap songs. The phone has a shuffle feature which plays each song once in a random order without repeating a song until all of the songs in the playlist have played. If Megan listens to the playlist on shuffle, what is the probability that the first song is a rock song and the second song is a rap song? A 25 198 149 198
An experiment consists of rolling a pair of fair dice, one red and one green. An outcome is an ordered pair (r,g), where r is the number on the red die and g is the number on the green die. List all outcomes of this experiment.
Suppose a system will work if any one of the 10 different components work. The probability that a particular component works is 0.222, independently of all the other components. Find the probability that the system works.

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