Please answer #21 and explain your reasoning! | 14 3/4"L 118 7/8be the transition matrix for a regular Markov chain. Find w2, the second20 Let P=coordinate of the stable vector for this Markov chain.a) 67b) 17c) 18d) 7/8e) none of the others21. Let E, F, and G be events in a sample space S and suppose Pr[E] = Pr[F] = Pr[G] = .5,PrEOFOG] = PHE'OFOG]= PHE nF n Gʻ) = 2, and Pr[EnFnG]=.1. What isa) 2 b) 1c) not enough information d) 3 e) none of the others22 Sam's Sub Shoppe uses a linear relationship, based on length, to determine the selling priceof a sub sandwich. If a 5 inch sub sells for $3.50 and an 8 inch sub sells for $5.30, what is theprice of a two-foot sub?a) $15.90b) $16.90e) $19.95d) $14.90e) none of the others23 The SKI-HI Junk Bond Company classifies each week's sales volume as high (H) or veryhigh (V). Data indicates that the week-to-week changes in volume follow the pattern of aMarkov chain with states H and V and the transition probabilities are as follows:Transition ProbabilityH→H3H+ V.7V+H5V → VIf the current week's volume is high (H), what is the probability that it will be very high (V) 3weeks from now?a) 56b) 588c) 4d) 412e) none of the others24. A company buys 9 computers, and it plans to connect each pair of computers by a cable (onecable per pair). How many cables are needed?a) 18b) 72c) 9!d) 36e) none of the others25. A bucket contains 3 red balls and 2 blue balls. Two balls are drawn simultaneously and atrandom. What is the probability that one ball is blue, given that at least one ball is red?a) 13b) 23c) 25d) 35e) none of the others

Event: In probability theory, an event is an outcome or a set of outcomes of a random experiment to which a probability is assigned. A single outcome is an element of a sample space and different events in a random experiment are generally not equally likely, since they may include very different groups of outcomes. Complement of an Events: The complement of an event A, written as Ac, is defined as the non-occurrence of event A. General Probability Addition Rule: For any two events A and B, the probability of occurrence of A or B is given by,We have, P(E'∩F'∩G)+P((E'∩F'∩G')=0.2+0.1⇒P(E'∩F')=0.3 [since P(A∩B)+P(A∩B')=P(A)] Similarly, P(E'∩G')=P(F'∩G')=0.3 Also, P(E)=0.5⇒1-P(E)=1-0.5⇒P(E')=0.5 Similarly, P(F')=P(G')=0.5 Now, P(E∩F∩G)=1-P(E∩F∩G)'=1-P(E'∪F'∪G') [by De-Morgan's law]=1-P(E')+P(F')+P(G')-P(E'∩F')-P(F'∩G')-P(G'∩E')+P(E'∩F'∩G')=1-(0.5+0.5+0.5-0.3-0.3-0.3+0.1)=1-0.7=0.3 Answer: The correct answer is: Option d). Therefore, all other options are incorrect.

Math

Probability

21. Let E, F, and G be eventa in a sample space S and suppose Pr[E) = Pr[F] = Pr(G] = .5, PHEOFOG) = PHE'OFOG)=PrEnF nG)= 2, and PrfEOFnG]=.1. What is a) 2 b) 1 c) not enough information d) 3 e) none of the others

21. Let E, F, and G be eventa in a sample space S and suppose Pr[E) = Pr[F] = Pr(G] = .5, PHEOFOG) = PHE'OFOG)=PrEnF nG)= 2, and PrfEOFnG]=.1. What is a) 2 b) 1 c) not enough information d) 3 e) none of the others

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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