There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal. The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one o the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left or the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one? Hints: Find the solution by using Bayes' theorem, calculating all the conditional probabilities involved. Start calculating the probability of having Gold in our hands Page 5 of 7 given that we know that the host unwraps Silver, P(G|Hs) = . . Then compare with the probability of having Bronze or Wood in our hands given that we know that the host unwraps Silver, P(B\Hs) = . . ., P(W\Hs) = . .....
There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are all wrapped with dark wrapping paper, such that it is impossible to distinguish them. You would like to find the gold medal. The game starts as follows. You pick one medal without unwrapping it, and then the game host unwraps one o the remaining medals and reveals that it is a silver medal. (Assume here that the host unwraps a medal with equal probability, but knowing where the gold medal was and avoiding unwrapping the gold medal if still on the table, to keep the game interesting to watch until the end.) You have now three medals left to unwrap (one in your hand, two on the table). At this point, the host gives you the option to change your mind and swap your medal for one of the two left or the table. What would you do at this point? Would you keep your medal, or swap it with one of the two medals left on the table? If so, which one? Hints: Find the solution by using Bayes' theorem, calculating all the conditional probabilities involved. Start calculating the probability of having Gold in our hands Page 5 of 7 given that we know that the host unwraps Silver, P(G|Hs) = . . Then compare with the probability of having Bronze or Wood in our hands given that we know that the host unwraps Silver, P(B\Hs) = . . ., P(W\Hs) = . .....
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:Statistics and Probability
There are four medals (Gold, Silver, Bronze and Wood) on a table, but they are
all wrapped with dark wrapping paper, such that it is impossible to distinguish
them. You would like to find the gold medal. The game starts as follows. You
pick one medal without unwrapping it, and then the game host unwraps one of
the remaining medals and reveals that it is a silver medal. (Assume here that the
host unwraps a medal with equal probability, but knowing where the gold
medal was and avoiding unwrapping the gold medal if still on the table, to keep
the game interesting to watch until the end.) You have now three medals left to
unwrap (one in your hand, two on the table). At this point, the host gives you
the option to change your mind and swap your medal for one of the two left on
the table. What would you do at this point? Would you keep your medal, or
swap it with one of the two medals left on the table? If so, which one? Hints:
Find the solution by using Bayes' theorem, calculating all the conditional
probabilities involved. Start calculating the probability of having Gold in our
hands Page 5 of 7 given that we know that the host unwraps Silver, P(G|Hs) = . .
. Then compare with the probability of having Bronze or Wood in our hands
given that we know that the host unwraps Silver, P(B|Hs) = . . ., P(W\Hs) = ..
.....
. ..
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