Since we just had a geometric puzzle, let's go numerical this time:
1. A probability puzzle
By the time the movie started, there were 91 men and 121 women in the theater. If the first moviegoer to enter the theater was a man wearing glasses, and the second was a woman not wearing glasses, then what is the probability that equal percentages of men and women in the theater were wearing glasses?
2. Fun(?) with fractions
I saw a survey in the newspaper once in which 33% of the people surveyed said "no" to something, while 67% said "yes." Whenever I see something like that, I always think, "Huh - I wonder if they only asked three people."
Well, suppose you saw it reported that 34% of people surveyed answered "no" to something, while 66% said "yes." What is the smallest number of people who could have participated in this survey? Assume that the people reporting these results have rounded their figures to the nearest whole percentage point.
I'll end with a graph that shows what the solution to puzzle #2 would be for any possible pair of percentages adding to 100%. Don't study the graph too carefully if you are going to solve the puzzle yourself!