The three doors, normal rules. On a game show, a contestant is told the rules as follows: There are three doors, labelled 1, 2, 3. A single prize has been hidden behind one of them. You get to select one door. Initially your chosen door will not be opened. Instead, the gameshow host will open one of the other two doors, and he will do so in such a way as not to reveal the prize. For example, if you first choose door 1, he will then open one of doors 2 and 3, and it is guaranteed that he will choose which one to open so that the prize will not be revealed. At this point, you will be given a fresh choice of door: you can either stick with your first choice, or you can switch to the other closed door. All the doors will then be opened and you will receive whatever is behind your final choice of door. Imagine that the contestant chooses door 1 first; then the gameshow host opens door 3, revealing nothing behind the door, as promised. Should the contestant (a) stick with door 1, or (b) switch to door 2, or (c) does it make no difference?
The three doors, normal rules. On a game show, a contestant is told the rules as follows: There are three doors, labelled 1, 2, 3. A single prize has been hidden behind one of them. You get to select one door. Initially your chosen door will not be opened. Instead, the gameshow host will open one of the other two doors, and he will do so in such a way as not to reveal the prize. For example, if you first choose door 1, he will then open one of doors 2 and 3, and it is guaranteed that he will choose which one to open so that the prize will not be revealed. At this point, you will be given a fresh choice of door: you can either stick with your first choice, or you can switch to the other closed door. All the doors will then be opened and you will receive whatever is behind your final choice of door. Imagine that the contestant chooses door 1 first; then the gameshow host opens door 3, revealing nothing behind the door, as promised. Should the contestant (a) stick with door 1, or (b) switch to door 2, or (c) does it make no difference?
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:The three doors, normal rules.
On a game show, a contestant is told the rules as follows:
There are three doors, labelled 1, 2, 3. A single prize has
been hidden behind one of them. You get to select one door.
Initially your chosen door will not be opened. Instead, the
gameshow host will open one of the other two doors, and he
will do so in such a way as not to reveal the prize. For example,
if you first choose door 1, he will then open one of doors 2 and
3, and it is guaranteed that he will choose which one to open
so that the prize will not be revealed.
At this point, you will be given a fresh choice of door: you
can either stick with your first choice, or you can switch to the
other closed door. All the doors will then be opened and you
will receive whatever is behind your final choice of door.
Imagine that the contestant chooses door 1 first; then the gameshow host
opens door 3, revealing nothing behind the door, as promised. Should
the contestant (a) stick with door 1, or (b) switch to door 2, or (c) does
it make no difference?
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