Probability Take-Home Exam Questions

from which urn you selected. However, you have the choice of replacing thefirst ball you selected before selecting the second, or keeping the first ballout and selecting a second ball from that same urn.What is your best strategy (with regards to replacing the first ball or keepingit out) to maximize your chances of guessing the urn correctly?14. Survivor Tribal Council (35 pts)In the tv reality game show of Survivor, tribes must regularly attend tribalcouncil where they vote to remove one of their members from the tribe andfrom the game. Let’s assume that two members have received all the votes.There are a votes for Person A and b votes for Person B where a > b. ThusPerson A will be voted off the island.The host, Jeff Probst, reads the ballots one at a time to add excitement to theconclusion. Assume that he pulls the ballots randomly from the box. Whatis the probability that the vote count is tied at some point after the first ballothas been read?15. Survivor Fix (45 pts)Read the above question about voting in Survivor. If you have watched thisshow regularly, there seems to be an unusually large number of ties when thevotes are read ”in a random order”. That last vote always seems to be the decidingfactor. Certainly the producers cannot alter the votes since that wouldviolate the integrity of the game. However, it is rumored that the order inwhich the ballots are read is not random and that the order is selected to addextra suspense to the last vote.Research the vote-reading outcomes from the previous Survivor episodesand then determine the probability that the order is purposely manipulated toadd more drama for the tv viewing audience.This will require some additional reading material in Bayesian analysis andalso some time invested in researching survivor voting.6