Attention all Mlodinowsters! (ahem…I would knock off this quiz in a minute, if I wasn’t busy tracking down that ‘Arnold Stang vs Super-Mechagodzilla’ video!)
Mr. Mlodinow, a visiting lecturer at Cal Tech and co-author of “A Brief History of Time” with Stephen Hawking, peppers “The Drunkard’s Walk,” set to be published next month, with dozens of examples, ranging from historical to personal to newsy. They serve to sketch an engaging history of probability and statistics, and to bolster his underlying thesis that the randomness that afflicts a sot’s amblings is pervasive in our lives. Furthermore, Mr. Mlodinow argues, we often act as if under the influence, failing to recognize the randomness in patterns and the patterns in randomness.
1. Suppose 1,000 athletes are tested for drugs. One in 10 have used the drugs, and the test has a 1% false-positive rate (and the false-negative rate is negligible). If an athlete from this group tests positive, what is the probability that she has used the drugs, to the nearest percentage point?
4. In baseball, suppose the American League champion is better than the National League champion, such that it has a 55% probability of winning each game against the NL champ. Then the NL champ nonetheless will win a best-of-seven-games series four in 10 times. What is the smallest odd number, X, for which a World Series between these two league champs that is best-of-X will ensure that there’s a 95% probability of a just result — the superior AL champ winning?