Some of the problems posed in this paper have been passed around the scientific community for several years and have served to jar a good many scientists regarding their intuition for statistical events. Since these problems are part of the scientific folklore, it seems worthwhile to write them down. The informal narrative style used reflects an attempt to capture a part of the spirit of the usual oral presentation. The author has added some additional questions and methods of solution that have arisen in presenting the problems to informal colloquiums.