This Mind Muddler addresses how to interpret the results when a contestant on the show “Who Wants To Be A Millionaire” asks an audience of 100 members for help.

It asked how many votes the most popular answer to the question must receive so that the probability that it is correct is at least 50%, 90% and 99% respectively. The answers are 30, 34 and 38 votes respectively. Slightly different interpretations of the problem (such as assuming “most popular” would allow ties also) change the answers slightly.

The second part of the muddler asked problem-solvers to compute the probability that the correct answer gets the most votes supposing a certain number of audience members know the right answer and the rest vote randomly. When only five people know the answer, the probability that the correct answer receives the most votes is 51.99%. When ten people know the correct answer, the probability
jumps to 81.61%.