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) = . .....
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 61E: Roulette American roulette is a game in which a wheel turns on a spindle and is divided into 38...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage