Answer to 2. The second probability would be vastly higher. To see this, let me make up some illustrative numbers. There are about four million innocent people in the area and, we'll assume, one guilty one. Let's estimate that 10 people (including the guilty one) own all the three of the items mentioned above. The first probability — that an innocent man owns all these items — would be 9/4,000,000 or less than 1 in 400,000. The second probability — that a man owning all three of these items is innocent — would be 9/10. Whatever the actual numbers, these probabilities usually differ substantially. Confusing them is dangerous (to defendants).
Answer to 3. For the World Series to last 6 or 7 games, it must last at least 5 games, at which point one team would be ahead 3 games to 2. If the team that is ahead wins the 6th game, the Series is over in 6 games. If the team that is behind wins the 6th game, the Series goes to 7 games. Since the teams are equally matched, the Series is equally likely to end in 6 or 7 games.
Answer to 4. The solution requires that we use a bit of probability theory. Doing so, we find that, on average, team A will play 2.9375 games at its home stadium and team B 2.875 games at its home stadium. Thus team A is a bit more likely to play at home.
Answer to 5. Even given the absurdly generous assumptions above, there would be 110,000 undecided voters (1 percent of 11 million). The probability of a 100 percent vote is thus equal to the probability of flipping a fair coin 110,000 times and having heads come up each and every time! The probability of this is 2 to the power of minus 110,000, or a 1 preceded by more than 30,000 0's and a decimal point. This would be the cosmic mother of all coincidences!
Answer to 6. As of this writing the Democrats hold a one vote edge in the Senate, and there are a number of races too close to call. Significant consequences will surely flow from small, but unpredictable factors so my prediction won't be ready until Wednesday, Nov. 6.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the forthcoming A Mathematician Plays the Market, which will be published in the spring. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.