17 - Example: Sequential Quiz Show I

Summary

Prerequisites: Chapters 8, 12, and 16.

Pre-Class Activity: Every student should bring a hard multiple-choice question with five choices for answers from another class.

SEQUENTIAL QUIZ SHOW(n, m): Three players, Ann, Beth, and Cindy, have a difficult multiple choice question with five choices. Starting with Ann and continuing cyclically, the player whose move it is can answer or wait. If the player answers correctly, the player gets $n. If the answer is incorrect, the player pays $m and is out of the game. If the player waits, the quiz master reveals a wrong answer (decreasing the number of choices by one), and the next player moves.

Student Activity Play the game several times, using the questions brought to class.

Candidates with Little Knowledge

It is easy to play the game well if you know the right answer: give it when it is your turn. In the remainder of this chapter we will show how to play the game if the players don't know the right answer. We assume that the question is so difficult that the players don't know which choice is right, nor can they rule out any of them of being right. So, for the players each of the answers has probability 1/5. All they can do is guess.

Although the procedure of revealing some wrong answers by the quiz master may recall the Monty Hall paradox, it is not related to it. After an answer has been revealed as wrong, either by a candidate betting on it or by the quiz master when a candidate waits, the probability of being right increases for the remaining answers uniformly. This is different from the Monty Hall paradox. Whenever a candidate faces, for instance, three choices, each could be right with probability 1/3.