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On a quiz show, a contestant stands at the entrance to a maze that opens into two rooms, labeled A and B in the figure. The master of ceremonies' assistant is to place a new car in one room and a donkey in the other. The contestant must walk through the maze into one of the rooms and will win whatever is in that room. If the contestant makes each decision in the maze at random, in which room should the assistant place the car to give the contestant the best chance to win? Entrance A Understanding the Problem The contestant must first choose one of the paths at the entrance and then choose another path as she proceeds through the maze. To determine the room the contestant is most likely to choose, the assistant must be able to determine the probability of the contestant's reaching each room. Devising a Plan: One way to determine where the car should be placed is to model the choices with a tree diagram and to compute the probabilities along the branches of the tree. Carrying Out the Plan: 1. Draw a tree diagram for the maze, along with the possible outcomes and the probabilities of each branch. 2. Calculate the probability of the event that room A is chosen

On a quiz show, a contestant stands at the entrance to a maze that opens into two rooms, labeled A and B in the figure. The master of ceremonies' assistant is to place a new car in one room and a donkey in the other. The contestant must walk through the maze into one of the rooms and will win whatever is in that room. If the contestant makes each decision in the maze at random, in which room should the assistant place the car to give the contestant the best chance to win? Entrance A Understanding the Problem The contestant must first choose one of the paths at the entrance and then choose another path as she proceeds through the maze. To determine the room the contestant is most likely to choose, the assistant must be able to determine the probability of the contestant's reaching each room. Devising a Plan: One way to determine where the car should be placed is to model the choices with a tree diagram and to compute the probabilities along the branches of the tree. Carrying Out the Plan: 1. Draw a tree diagram for the maze, along with the possible outcomes and the probabilities of each branch. 2. Calculate the probability of the event that room A is chosen

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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On a quiz show, a contestant stands at the entrance to a maze that opens into two rooms, labeled A and B in the figure. The master of ceremonies' assistant is to place a new car in one room and a donkey in the other. The contestant must walk through the maze into one of the rooms and will win whatever is in that room. If the contestant makes each decision in the maze at random, in which room should the assistant place the car to give the contestant the best chance to win? Entrance B A Understanding the Problem The contestant must first choose one of the paths at the entrance and then choose another path as she proceeds through the maze. To determine the room the contestant is most likely to choose, the assistant must be able to determine the probability of the contestant's reaching each room. Devising a Plan: One way to determine where the car should be placed is to model the choices with a tree diagram and to compute the probabilities along the branches of the tree. Carrying Out the Plan: 2. Calculate the probability of the event that room A is chosen 1. Draw a tree diagram for the maze, along with the possible outcomes and the probabilities of each branch.
Transcribed Image Text:On a quiz show, a contestant stands at the entrance to a maze that opens into two rooms, labeled A and B in the figure. The master of ceremonies' assistant is to place a new car in one room and a donkey in the other. The contestant must walk through the maze into one of the rooms and will win whatever is in that room. If the contestant makes each decision in the maze at random, in which room should the assistant place the car to give the contestant the best chance to win? Entrance B A Understanding the Problem The contestant must first choose one of the paths at the entrance and then choose another path as she proceeds through the maze. To determine the room the contestant is most likely to choose, the assistant must be able to determine the probability of the contestant's reaching each room. Devising a Plan: One way to determine where the car should be placed is to model the choices with a tree diagram and to compute the probabilities along the branches of the tree. Carrying Out the Plan: 2. Calculate the probability of the event that room A is chosen 1. Draw a tree diagram for the maze, along with the possible outcomes and the probabilities of each branch.
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