7. A student has three routes of getting to his school: A, B, and C. Each day he picks one, and hischoice is influenced only by his previous day choice:– if he takes route A today, then he will take route A, B, or C next day with respective1 1probabilities,244- if he takes route B today, then he will take route A, B, or C next day with respective1probabilities, 0, 2- if he takes route C today, then he will take route A, B, or C next day with respective1probabilities3'4'12'(a) Formulate this as a Markov chain by defining its states and giving its (one-step) transitionmatrix.(b) Find the n-step transition matrix P(n)=2 and 20.(c) If he takes route A today, what is the probability that he will take route A in 2 the dayafter tomorrow?(d) The probability that he takes route A today is 0.4. Use the results from part (b) to determinethe probability that he will take route B 20 days from now.i=0(a) Use equations лP = π, Σ²0¹₁ = 1 to find the steady state probabilities. Are theprobabilities consistent with the numbers in P (20)?

As per our guidelines. we are supposed to answer only 3 sub-parts. a) The states of this Markov…

Answered: 7. A student has three routes of…

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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4. A merchant stocks a certain perishable item. He knows that on any given day, he will have a demand for either 2, 3, or 4 of this items with probabilities 0.1, 0.4 and 0.5 respectively. What is the average daily demand?
The probability that Taylor Swift is Austin’s favorite music artist is .10. The probability that he will go to one of her concerts is .84. However, the probability that he does not like Taylor Swift and will go to a concert (because his wife makes him) is .75. a.) Write down the 3 pieces of information given in terms of probabilities involving event A (Taylor Swift is Austin’s favorite music artist) and event B (Austin will go to a Taylor Swift concert). b.) Summarize the above information using a probability table. c.) Find the probability that Taylor Swift is Austin’s favorite music artist or Austin will go to a Taylor Swift concert.
Suppose that Trendy Inc. products a style of a seasonal business suit, Sit-T-Slicker, which has a cost of $500 per unit. The demand during the season for Sit-T-Slicker is generally unknown and could be either: 200, 500, 800, 1100, and 1500 units with equal probabilities. Trendy sells the Sit-T-Slicker suit for $900 per unit during its three-month season, and for $300 per unit when sold after that time. Given the above data, what is the optimal order quantity for the Sit-T-Slicker? What is expected profit? Suppose the probabilities in part a change to 0.05, 0.25, 0.40, 0.25, 0.05 for demand levels 200, 500, 800, 1100, 1500, respectively. What is the optimal order quantity and expected profit in this case? How would better information regarding the demand for the Sit-T-Slicker suit change the data provided in this problem? How would this information affect the answers to part a? Explain.
6. A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10% possess both symptoms, and the remainder have neither symptoms. For one person chosen at random from this group, find these probabilities (a) The person has neither symptom. (b) The person has at least one symptom. (c) The person has both symptoms, given that the person has symptom B.
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Omar commutes from his home to Concordia by car. To try to get to his class on time, he tries different routes to get to Concordia but heavy traffic and construction keeps occurring randomly along his four favourite routes: routes A, B, C, and D, which he takes with probabilities of 0.4, 0.15, 0.3, and 0.15, respectively. If he takes route A then he is on time for class with a probability of 0.7, if route B then he is on time with probability 0.9, if route C then he is on time with probability 0.8, and if route D then he is on time with probability 0.6. (a)What is the probability that Omar arrives to class on time? (b) If Omar arrives to class on time, what is the probability that he took route A?
Suppose you’re playing Texas Hold ’Em Poker, and you are dealt a hand witha Jack of Clubs and a Queen of Hearts. The river of 5 cards hasn’t been dealtyet, and you’re hoping to get a straight (5 cards with consecutive ranks, such as10,J,Q,K,A or 8,9,10,J,Q). What is the probability that you will get a straightthat uses both the Jack and Queen in your hand? (This last part is to keep theproblem simple, since it’s possible to get a straight that uses neither card in your hand, suchas A,2,3,4,5, all in the river. Besides, in those cases, ALL players would have a straight, sothat’s not so good for you!)Guide: Our goal is to calculate:P(straight using both cards in hand) = # 5-card combinations that get us a straight with the J & Q# 5-card combinations overall .(a) We’ll start with the denominator, which can be done with a singleformula from class: How many 5-card combinations are possible for theriver? (Keep in mind what is in your hand. Note that how many opponents you haveand what…

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