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 1 1probabilities 2 4 4- if he takes route B today, then he will take route A, B, or C next day with respectiveprobabilities, 0,- if he takes route C today, then he will take route A, B, or C next day with respective1 1 5probabilities 234(a) Use equations лР = π, Σ₁₁¹₁ = 1 to find the steady state probabilities.

From the given information, there are three routes of getting to school. If a student takes route A…

Answered: A student has three routes of getting…

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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An amount of $10,000 is to be invested for three years. The yield rate for the first year will be equally likely to be 5%, 6%, 7%, 8% or 9%; for the second year will be equally likely to be 7% or 9%; for the third year will be 7%, 8% or 9% with probabilities 0.3, 0.5 and 0.2, respectively. The yield rates in different years are independent. Find the probability that the accumulation of the investment for the three years will be greater than its expected value.
If two cards are drawn without replacement from an ordinary deck, find the probabilities of the following results An ace and a 4 are drawn.
In a manufacturing process, lots having 10%, 12%, 14% or 16 defectives are produced according to the respective probabilities 0.2, 0.35, 0.15 and 0.3. Three customers have contracts to receive lots from the manufacturer. The contracts specify that the percentages of defectives in lots shipped to customers A, B and C should not exceed 10, 12 and 14, respectively. If a lot has a higher percentage of defectives that stipulated, a penalty of $ 200 per percentage point is incurred. On the other hand, supplying better quality than required costs the manufacturer $150 per percentage point. If the lots are not inspected prior to shipment, which customer should have the highest priority for receiving the order?
7. PAGASA is planning to place at five rain gauge in different locations within Metro Manila. The rain gauge in different location R1, R2, R3, R4 and Rs will operate 0.45, 0.30, 0.20, 0.25 and 0.30, respectively, at a time. If rain pours in those locations has probabilities of 0.2, 0.1, 0.3, 0.2, and 0.2, respectively, what is the probability that it will operate and measure rain water?
(QUEEN'S SECRET AND GENIES) In old days, there was a queen and she had a secret problem to solve. To get an answer to her secret problem, the queen bought one female and one male genie lamps. The probabilities that her secret problem can be solved by the male and female genies are 0.3 and 0.4 respectively. A Queen looking for divine help. Assume the queen keeps the genies independently away from each other with a fear that both could not harm her, what is the probability that the queen's secret problem is solved by at least one of the genies? Note: Please keep accuracy upto two decimal places.
Adam, Bill, Carl, David, Ellen, Fran and Ginger are all candidates for two different jobs, a supervisor and a deputy. If two candidates from this list are selected randomly and the first person selected gets the supervisor job while the second person gets the deputy job, compute the probabilities of the following events: (i) Two males are selected (ii) Two females are selected (iii) One male and one female is selected (iv) Adam is chosen for one of the two jobs (v) Adam is chosen to be the supervisor
Write the m.g.f. of a r.v. X taking on values -4, 0 and 4 with respective probabilities 0.3, 0.4, and 0.3. 0.3 e4 +0.4 • e² + 0.3 -4z 0.3 e +0.4+ 0.3. e4z 1+0.3. e4z +0.3 · e-4z e4 0.3 ez +0.4 e² + 0.3. e4z
Hey! Need help with the following problem, thank you! Contains three parts (a-c).
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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