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: 4. Determine which room (A or B) the car should be placed for the contestant to have the best choice of winning it? Explain.
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: 4. Determine which room (A or B) the car should be placed for the contestant to have the best choice of winning it? Explain.
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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Read the paper above and answer question # 4 only
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:
4. Determine which room (A or B) the car should be placed for the contestant to have the best choice
of winning it? Explain.
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