Probability and risk increasingly permeate our lives. Like it or not, we must be able to assess the threats and opportunities that face us. Here's a random sampling of half a dozen hypothetical questions (with answers at the end) inspired by a variety of recent news stories.
1. It's impossible to say with any precision what risk the Washington area snipers posed to individuals in suburban Maryland and Virginia, but certainly the likelihood of being attacked was quite small — 13 victims out of about four million people in the affected area over three weeks.
Our psychology, however, leads us to be more afraid of what's unfamiliar, out of our control, dramatic, omnipresent, or is the consequence of malevolence. On all these counts, the snipers were more terrifying than more common risks.
Still, let's consider one of these more common risks. How many traffic fatalities can be expected to occur in any given three-week period in the United States? How many in an area the size of suburban Washington?
2. Early in the sniper case the police arrested a man who owned a white van, a number of rifles, and a manual for snipers. It was thought at the time that there was one sniper and that he owned all these items, so for the purpose of this question let's assume that this turned out to be true.
Given this and other reasonable assumptions, which is higher — a.) the probability that an innocent man would own all these items or b.) the probability that a man who owned all these items would be innocent?
3. The Anaheim Angels and San Francisco Giants were in this year's World Series. The series ends, of course, when one team wins four games.
Is such a series, if played between equally capable opponents, more likely to end in six or seven games?
4. The rules of the series stipulate that team A plays in its home stadium for games 1 and 2 and however many of games 6 and 7 are necessary, whereas team B plays in its home stadium for games 3, 4, and, if necessary, game 5.
If the teams are evenly matched, which team is likely to play in its home stadium more frequently?
5. Eleven million people went to the polls recently in Iraq and, the Iraqi news media assure us, 100 percent of them voted for Saddam Hussein for president. Let's just for a moment take this vote seriously and assume that Hussein was so wildly popular that 99 percent of his countrymen were sure to vote for him and that only 1 percent of the voters were undecided. Let's also assume that these latter people were equally likely to vote for or against him.
Given these assumptions, what was the probability of a unanimous 100 percent vote?
6. Politics in a democracy is vastly more complicated than it is under dictatorships. Witness the upcoming elections here.
What is the probability that the Republicans, the Democrats, or neither will take control of the Senate on Nov. 5?
Answer to 1. There are approximately 40,000 auto fatalities annually in this country, so in any given three-week period, there would be about 2,300 fatalities. The area around Washington has a population of about four million, or 4/280 of the population of the U.S., so as a first approximation, we could reasonably guess that 4/280 times 2,300, or about 30 auto fatalities, would occur there during any three-week period. Attention must then be paid to the ways in which this area and its accident rate are atypical.