# Alarmist Numbers: Female Happiness, Containing Fires and Health Care Satisfaction

The containment figure is determined by the fraction of the approximate perimeter of the fire that has a "fire line" cleared along it. So if the fire is estimated to have a perimeter of 20 miles and along 8 miles of that perimeter there is a fire line or trench that's been dug, then the fire is said to be 8/20 or 40 percent contained.

Often absurdly precise figures for the percent of containment are given, but the figure is very approximate since the fire and hence its perimeter could be growing rapidly.

And there are 640 acres in a square mile. My guess is that only a tiny fraction of Americans know this, which makes the media's use of the term unnecessarily, but possibly intentionally, alarmist.

What sounds worse: In the hills there are 23,000 acres ablaze or there is a roughly square area 6 miles on a side that is burning.

#### A World Series Question

It's October, so let me interpose here a question on the World Series. The answer appears at the end of this column. Imagine that the opposing teams are evenly matched and that the probability of either one of them winning any given game is 50 percent.

In a best of seven series, whichever team wins four games is the winner and so the series might end in 4 games, in 5 games, or may take 6 or 7 games. Without conducting any sort of calculation, determine if the series is more likely to end in 6 or 7 games.

### Overstating Satisfaction with Medical Insurance

Moving on to another incendiary issue, I note that opponents of health care reform often cite surveys showing that most people are quite satisfied with their insurance and medical care.

The satisfaction rate is likely to be artificially high, however, since relatively few of the people surveyed are seriously ill and so they don't place any significant demands on the system.

When surveys are taken, it might be better to focus on this more telling reference class, those seriously ill people who've actually needed considerable help from their insurance companies or who were not insured at all.

By analogy people with no strong opinions about anything are likely to think that the right to free speech is secure. Just as it's crucial to uphold the right to free speech of someone who is actually saying something unpopular, so it is to guarantee the right to health care of someone who is actually very sick.

Relevant to this last is a recent study by researchers at Harvard who estimate that there are approximately 45,000 deaths annually due to lack of insurance coverage. There are a number of methodological problems in conducting such a study, but a previous commonly cited estimate was 18,000 annual deaths.

#### Numbers Are to Be Debated, Deconstructed

The Harvard study noted that the risk of death for those without health insurance was 25 percent greater than for those with insurance in 1993, but that the figure has risen to 40 percent now.

A partial explanation is the uninsured have a harder time getting treatment, which has improved over the years, because strapped hospitals have reduced their services to the poor.

The bottom line for these as well as most numerically flavored stories in the news is that numbers can and should be examined, deconstructed, debated, and put into context.

Answer to World Series question: For the series to end in 6 or 7 games, it must last at least five games, at which point, one team, call it A, will have won 3 games and the other team, B, just 2.

If A wins the 6th game, the series is over after 6 games, but if B wins the 6th game, the series moves on to the 7th game. Since these possibilities are equally likely (remember A and B each have a 50 percent probability of winning any given game), it's equally likely that the series will end in 6 or 7 games.

John Allen Paulos, a professor of mathematics at Temple University in Philadelphia, is the author of the best-sellers, "Innumeracy" and "A Mathematician Reads the Newspaper," as well as (just out in paperback) "Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up." His "Who's Counting?" column on ABCNews.com appears the first weekend of every month.

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