2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at randomone of the doors out of the room.1234560Suppose we remove the trap and another rat enters the maze starting in room 1. What is the expectedtime to return to room 1?

Given that a rat runs through the maze shown below, at each step it leaves the room it is in by…

Answered: 2. A rat runs through the maze shown…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.5: Counting Principles

Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...

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A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in the front and 3 in the back a. How many arrangements are possible with no restrictions? b. How many arrangements are possible if the parents must sit in the front? C. How many arrangements are possible if the parents must be next to each other?
Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered 1-36, of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on three consecutive spins.

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2. A rat runs through the maze shown below. At each step it leaves the room it is in by choosing at random one of the doors out of the room. 1 2 3 4 5 6 Suppose we remove the trap and another rat enters the maze starting in room 1. What is the expected time to return to room 1?