Question

A mouse is placed in room 5 of the maze shown to the right. At each step, the mouse exits the particular room that it is in, and is equally likely to choose any of the available doors to leave.

(a) Consider the mouse's starting position in room 5. Calculate the probability that the mouse will exit through door 4 on its first move.

(b) Calculate the probability that the mouse will exit through door 2 on its second move, given that it exited through door 4 on the first move.

(c) Determine the probability that the mouse will exit through door 1 on its third move, given that it exited through door 4 on the first move and door 2 on the second move.

Answer 1

To find the probabilities of the mouse's movements through the maze, one must consider the number of doors in each room and the concept of conditional probability. The specific probabilities cannot be determined without a visual representation of the maze.

Step-by-step explanation:

To solve the student's question about probabilities related to a mouse moving through a maze, we must consider the rules of conditional probability and the structure of the maze provided. Since a visual diagram of the maze is not included in the question, we can only provide a generic approach to calculating such probabilities.

(a) To calculate the probability that the mouse will exit through door 4 on its first move from room 5, you would count the number of doors in room 5 and determine the likelihood of choosing door 4 as a fraction of the total number of doors.

(b) The probability that the mouse will exit through door 2 on its second move, given it exited through door 4 on the first move, will depend on the number of doors in the room that the mouse enters after moving through door 4.

(c) Finally, determining the probability that the mouse will exit through door 1 on its third move, given the previous moves, would require knowing the room the mouse is in after the second move and the available doors.