There are four medals (Gold, Silver, Bronze and Wood) on a table, but they areall wrapped with dark wrapping paper, such that it is impossible to distinguishthem. You would like to find the gold medal.The game starts as follows. You pick one medal without unwrapping it, and thenthe game host unwraps one of the remaining medals and reveals that it is a silvermedal. (Assume here that the host unwraps a medal with equal probability, butknowing where the gold medal was and avoiding unwrapping the gold medal ifstill 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 yourmedal 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 oneof the two medals left on the table? If so, which one?Hints: Find the solution by using Bayes theorem, calculating all the conditionalprobabilities involved. Start calculating the probability of having Gold in our handsgiven that we know that the host unwraps Silver, (|) = . . ..Then compare with the probability of having Bronze or Wood in our hands given

Page 5 of 7that we know that the host unwraps Silver, (|) = . . .., (|) = . . .