Quiz Question Alice and Bob are sitting directly across from each other at a circular table withsix chairs. They decide to move chairs.At each step, Alice and Bob will move according to the following rules.AliceBob(1) Alice chooses a chair randomly, which is equally likely to be the chair on her left, the chairon her right, or her current chair. Independently, Bob also chooses a chair randomly,which is equally likely to be the chair on his left, the chair on his right, or his currentchair.Alice’s choice of chair at this step is unaffected by where Bob is sitting, and similarly forBob’s choice of chair.(2) Then Alice and Bob compare their choices. If they have chosen the same chair, then Aliceand Bob do not move. Otherwise, if they have chosen different chairs, then they eachmove to the chair they chose.If Alice and Bob are sitting next to each other at the current step, and if they each choosethe other person’s chair, then they will swap chairs.Define Xn to be the distance between Alice and Bob, measured in terms of chairs, after n steps.This means: If Alice and Bob are sitting next to each other, then the distance is defined to be1. If Alice and Bob are sitting directly across from each other, the distance is defined to be 3.Otherwise the distance is defined to be 2. These three possibilities are illustrated below:AliceBobDistance 1Alice BobDistance 2AliceBobDistance 3The stochastic process (Xn, n = 0, 1, 2, . . . ) is a Markov chain with state space S = {1, 2, 3}.(a) Consider the situation where Alice and Bob are at state Xn = 3 (i.e., across from eachother). What are the way(s) they could choose chairs in order to reach state 1 (i.e., besideeach other) after one step? What is the probability of this happening? Which transitionprobability have you just found?(b) What are the way(s) they could choose chairs in order to stay at state 3 after one step?What is the probability of this happening? Which transition probability have you justfound?(c) Part of the transition matrix is given below. Fill in the missing entries.P =6/92/9 2/94/92

Select the correct answerCertain number of chairs (more than 5) are placed around the circular table, facing towards the centre. Some of the chairs are vacant and some chairs are occupied by person. Distance between 2 chair placed adjacent to each other is in consecutive multiplies of 3 metres, when we move in clockwise direction, starting from the chair of person A. Circumference of the circle is 189 meters.A is sitting on the chair 2nd to the left of the chair of F, who is sitting on the chair to the immediate left of P. Only 1 chair is placed between the chair of A and chair of M, who is sitting on the chair to the immediate right of N. B is sitting on the chair neither adjacent to A nor adjacent to P.How many chairs are placed around the table?Options68Cannot be determined97

Directions: Study the following information and answer the given question. A,B,C,D,E and F are seating around a circular table. A is between E and F, E is opposite to D and C is not in either of the neighbouring seats of E.Who is opposite to B?CDFNone of these

Select the correct answerStudy the following information and answer the given questions Sixteen chairs are seated around two concentric circular tables, containing equal number of chairs in each. There is equal distance between consecutive chairs on each table. Some people are facing inward while others are facing outward. Two seats in each table are vacant. 4 chairs (2 on outer table and 2 on inner table) each are along the same line. Note: 2 people facing same direction means either both are facing inside or both are facing outside. 2 people facing opposite direction means if one is facing inward, the other is facing outwards and vice versa Three chairs are arranged between K and H. Adjacent seats of H are vacant. P and A sit on different tables and face opposite directions. On the outer table where P is sitting, P is the one closest to A. E, who faces the centre, sits third to the right of A. S sits to the immediate left of P. Only two persons seated at the outer table are facing outward. K who sits on the outer table is closest to L who sits on inner table. L sits in a seat which is third from G's seat when counted in anti-clockwise direction. L faces the opposite direction of A K faces the centre. G sits adjacent to A. M sits in a seat second to the left of L's seat. Q sits in a seat second to the right of the person's seat who faces an empty seat of the inner table. W and M are facing each other and are on different tables and closest to each other. I is an immediate neighbor of M. G and Q face the same direction, sitting in different tables. The immediate neighbors of M face the opposite directions. L and H face same direction. In which seat is M seated with respect to G’s seat?

Six boys A,B,C, D,E and F are sitting around a circular table as for the following conditions. F is sitting to the left of A. B is sitting between C and E and is opposite to A. E is sitting to the right of D. Q:If E interchanges his place with the person sitting opposite to B, then who sits to the right of E?

tudy the following information carefully and answer the questions given below. Eight persons A, B, C, D, M, N, O and P are sitting around a circular table facing the center with equal distances between each other (not necessarily in the same order). Each one of them is also related to N in some way or the other. 1) Only three persons sit between B and N. 2) Only one person sits between N and P. N's father sits to the immediate right of P. 3) N's sister sits third to the right of N's father. Only one person sits between N's sister and N's son. 4) M sits third to the left of N's son. Only three persons sit between M and N's husband. 5) A sits second to the right of N's husband. N's mother sits to the immediate right of C. C is not the husband of N. 6) N's daughter sits third to the right of P. 7) D sits to the immediate left of N's brother. Q3) How is B related to A?Choices:- Grand-mother Grand-father Grand-son Grand-daughter