Consider the Monty Hall gameshow problem. Contestants are given the option of picking 1 out of 3 doors, one door has a car behind it and the other 2 doors have goats. The contestant notices Monty has a physical tell that could indicate what prize is behind the door the contestant chooses. If the contestant initially chooses the door with the car, Monty will arch his left eyebrow with probability 4/5. If the contestant initially chooses a door with a goat, Monty will arch his eyebrow in the sameway with probability 1/4. (a) For each of the two strategies for the contestant - to switch or remain with their chosen door-draw a tree diagram to represent this variation of the Monty Hall problem. (b) Assuming the location of the car and the contestant's initial choice are both chosen uniformly at random, what is the probability that Monty gives his physical tell? (c) Suppose you are selected to be the next contestant on Monty Hall. You decide to go with the following strategy: If Monty arches his eyebrow after you select your door, you will stay with your initial door. Otherwise, you will switch. Use a tree diagram to illustrate your strategy and compute the probability that you win the car.
Consider the Monty Hall gameshow problem. Contestants are given the option of picking 1 out of 3 doors, one door has a car behind it and the other 2 doors have goats. The contestant notices Monty has a physical tell that could indicate what prize is behind the door the contestant chooses. If the contestant initially chooses the door with the car, Monty will arch his left eyebrow with probability 4/5. If the contestant initially chooses a door with a goat, Monty will arch his eyebrow in the sameway with probability 1/4. (a) For each of the two strategies for the contestant - to switch or remain with their chosen door-draw a tree diagram to represent this variation of the Monty Hall problem. (b) Assuming the location of the car and the contestant's initial choice are both chosen uniformly at random, what is the probability that Monty gives his physical tell? (c) Suppose you are selected to be the next contestant on Monty Hall. You decide to go with the following strategy: If Monty arches his eyebrow after you select your door, you will stay with your initial door. Otherwise, you will switch. Use a tree diagram to illustrate your strategy and compute the probability that you win the car.
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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Transcribed Image Text:Consider the Monty Hall gameshow problem. Contestants are given the option of picking 1 out of 3 doors, one door has
a car behind it and the other 2 doors have goats. The contestant notices Monty has a physical tell that could indicate
what prize is behind the door the contestant chooses. If the contestant initially chooses the door with the car, Monty
will arch his left eyebrow with probability 4/5. If the contestant initially chooses a door with a goat, Monty will arch his
eyebrow in the sameway with probability 1/4. (a) For each of the two strategies for the contestant - to switch or remain
with their chosen door- draw a tree diagram to represent this variation of the Monty Hall problem. (b) Assuming the
location of the car and the contestant's initial choice are both chosen uniformly at random, what is the probability that
Monty gives his physical tell? (c) Suppose you are selected to be the next contestant on Monty Hall. You decide to go
with the following strategy: If Monty arches his eyebrow after you select your door, you will stay with your initial door.
Otherwise, you will switch. Use a tree diagram to illustrate your strategy and compute the probability that you win the
car.
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VIEWStep 2: Construct the tree diagram to represent the variation of the Monty Hall problem.
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VIEWStep 4: Use a tree diagram to illustrate your strategy and compute the probability of winning the car.
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