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В Exit door Figure 1 Sigmund is investigating the behaviour of his pet mouse, Morty, in a maze. Figure 1 shows the maze with 4 rooms A, B, C and D. When Morty is in the maze, he car move around the maze leaving and entering rooms through two-way doors, shown in the diagram as When in a room, Morty leaves the room and enters the next room by choosing a door at random. He is equally likely to choose any door in the room, including the door through which he entered the room. Sigmund records a change of room as a move. So, A to B is one move, A to B to C is two moves. The investigation ends when Morty leaves room A by the Exit door. (a) Morty is placed in room A, as shown in Figure 1. () Write down the probability that the investigation will end after one move. (ii) Find the probability that Morty will be back in room A after two moves. (iii) Show that Morty is more likely to be in room C than to be in room A after two moves. In a second investigation, Morty is placed in room C. (b) Show that the probability that this investigation will end after three moves is 0.13 to 2 significant figures.

В Exit door Figure 1 Sigmund is investigating the behaviour of his pet mouse, Morty, in a maze. Figure 1 shows the maze with 4 rooms A, B, C and D. When Morty is in the maze, he car move around the maze leaving and entering rooms through two-way doors, shown in the diagram as When in a room, Morty leaves the room and enters the next room by choosing a door at random. He is equally likely to choose any door in the room, including the door through which he entered the room. Sigmund records a change of room as a move. So, A to B is one move, A to B to C is two moves. The investigation ends when Morty leaves room A by the Exit door. (a) Morty is placed in room A, as shown in Figure 1. () Write down the probability that the investigation will end after one move. (ii) Find the probability that Morty will be back in room A after two moves. (iii) Show that Morty is more likely to be in room C than to be in room A after two moves. In a second investigation, Morty is placed in room C. (b) Show that the probability that this investigation will end after three moves is 0.13 to 2 significant figures.

A First Course in Probability (10th Edition)
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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В Exit door Figure 1 Signund is investigating the behaviour of his pet mouse, Morty, in a maze. Figure 1 shows the maze with 4 rooms A, B, C and D. When Morty is in the maze, he can move around the maze leaving and entering rooms through two-way doors, shown in the diagram as When in a room, Morty leaves the room and enters the next room by choosing a door at random. He is equally likely to choose any door in the room, including the door through which he entered the room. Sigmund records a change of room as a move. So, A to B is one move, A to B to C is two moves. The investigation ends when Morty leaves room A by the Exit door. (a) Morty is placed in room A, as shown in Figure 1. (i) Write down the probability that the investigation will end after one move. (ii) Find the probability that Morty will be back in room 4 after two moves. (iii) Show that Morty is more likely to be in room C than to be in room A after two moves. In a second investigation, Morty is placed in room C. (b) Show that the probability that this investigation will end after three moves is 0.13 to 2 significant figures.
Transcribed Image Text:В Exit door Figure 1 Signund is investigating the behaviour of his pet mouse, Morty, in a maze. Figure 1 shows the maze with 4 rooms A, B, C and D. When Morty is in the maze, he can move around the maze leaving and entering rooms through two-way doors, shown in the diagram as When in a room, Morty leaves the room and enters the next room by choosing a door at random. He is equally likely to choose any door in the room, including the door through which he entered the room. Sigmund records a change of room as a move. So, A to B is one move, A to B to C is two moves. The investigation ends when Morty leaves room A by the Exit door. (a) Morty is placed in room A, as shown in Figure 1. (i) Write down the probability that the investigation will end after one move. (ii) Find the probability that Morty will be back in room 4 after two moves. (iii) Show that Morty is more likely to be in room C than to be in room A after two moves. In a second investigation, Morty is placed in room C. (b) Show that the probability that this investigation will end after three moves is 0.13 to 2 significant figures.
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