9. A rat runs through the maze shown below. At each step it leaves or stay by choosing at randomone of the doors with equal probability. For example, if it is in room 0, it can has two options:stay at room 0, or go to room 2 with equal probability of for each option. If it is in room 3, ithas three options: stay at room 3, go to room 2 or room 5 with equal probability of for eachoption.3+35a) Give the transition matrix P for this Markov chain.b)Find the stationary distributionc) Find the expected time to return to room 0.d)Now suppose that a piece of mature cheddar is placed on a deadly trap in Room 4. Themouse starts in Room O. Find the expected number of steps before reaching Room 4 forthe first time, starting in Room 0.

A Markov chain is given. Note: Hello! As you have posted more than 3 sub parts, we are answering the…

Answered: A rat runs through the maze shown…

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 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,
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?
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?
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
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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.
Please help!!! Q4. Ariana and Bella are playing a game. They each have 4 cards, which are numbered 1, 2, 3 and 4. Each shuffles her own cards and turns one over at random. If the cards show the same number, Ariana wins and Bella must pay Ariana $3. If the cards show different numbers, Bella wins and Ariana must pay Bella $1. By finding the probabilities of Ariana and Bella winning, show whether or not the game is fair.
Itranscript One male and one female dam rat pup were randomly selected from 8 litters to perform the swim maze. Each pup was placed in the water at one end of the maze and allowed to swim until it escaped at the opposite end. If the pup failed to escape after a certain period of time, it was placed at the beginning of the maze and given another chance. The experiment was repeated until each pup accomplished three successful escapes. The table to the right reports the number of swims required by each pup. Is there sufficient evidence of a difference between the mean number of swims required by male and female pups? Use a=0.01. Comment on the assumptions required for the test to be valid. B. t> Litter 1 2 3 OC. t 10 12 Female 11 [6526675 10
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.
A group of five students went to a hotel with 10 upper floors and a ground floor. The students simultaneously enter the elevator at the ground floor. The students choose their exit floors independently of each other. Determine the probability that they are all going to different floors when each student randomly chooses one of the 10 floors as their exit floor.
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try? Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws and must make both to win the game. What is the probability that Kay's team will win the game? Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number? (The formula is )
Sergio, Derrick, and Armando are creating a maze for there pet gerbil, Miguel. Sergio bets that Miguel will go straight when first entering the maze. Derrick bets that Miguel will turn right and Armando bets that Miguel will turn left. If there is an equal chance of Miguel taking one of the given paths, then what is the probability that Sergio or Armando will be correct? The probability that Sergio or Armando will be correct is_______?

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