A friend told me about a neighbor living in a small Pacific Northwest town who now dons a protective mask and rubber gloves when she gets and opens her mail.

Folks who consider such a fear of widespread anthrax contamination to be foolish may themselves purchase state lottery tickets, which operate with similar astronomical odds. The decisions we make in life generally occur after a conscious or unconscious computation of the cost/benefit ratio — the relationship between the biological and/or financial costs of the proposed action and the potential risks and benefits.

Lottery tickets have been called a tax on stupidity — the odds of winning being about the same whether we purchase or don’t purchase a ticket. And yet many intelligent people purchase lottery tickets because such a seemingly irrational decision may have at least a dollar’s worth of emotional value (where else can I buy three days of fantasy for a dollar?). It depends on how critical the dollar is to our financial status. Spending a single discretionary dollar on a lottery ticket is probably OK if it sparks a pleasant emotional fantasy, but someone in financial difficulty certainly shouldn’t spend 100 dollars on tickets in the naive belief that the odds have now sufficiently improved to anticipate a desperately needed payoff.

Donning a mask and gloves when the home mail arrives can similarly be emotionally OK, although rationally foolish. It’s probably OK to temporarily wear a mask and gloves if we consciously realize that we’re merely reducing irrational fears that have hijacked us. But it’s not OK to believe that anthrax contamination is a serious threat to the mail of regular folks in small town America. Is such contamination possible? Yes. Should we currently shape our behavior around that expectation? For most people, no.

The chances that something will occur depend on the number of possibilities and the randomness of the action. Flip a coin and the odds are 50/50 that it will be heads. If it comes up heads 100 flips in a row, the odds are still 50/50 that the next flip will be heads because only two possibilities exist and the flip is a random (unbiased) action. State lotteries seriously ratchet up the odds — select the correct six numbers out of a pool of 50 numbers in a random drawing, and the odds of winning zoom to well over 80 million to one.

Is the probability similar with anthrax contamination? Not necessarily. As with the coin toss, two possibilities exist: a given letter of the 600 million delivered each day will or won’t contain anthrax spores. But is mail contamination a random event (like a coin toss or lottery drawing)? Probably not. The contaminated letters thus far have been sent to high profile people in the media and government, and so potentially targeted folks and those who come into contact with such mail run a much higher risk of handling a contaminated letter than the rest of the population. They should take precautions (and especially with envelopes that seem suspicious), given the dangers involved in touching or breathing anthrax.

Why then would someone in a very low risk demographic group don mask and gloves? Because if the perpetrators decide to frighten even more people by shifting from targeted to randomly sent contaminated mail, everyone in the country will be equally at risk — and the danger is increased by cross-contamination (minute anthrax spores moving from letter to letter within the postal system). But still, the odds are hundreds of millions to one of getting such a letter.

Playing against high odds is generally an emotional and not a rational cost/benefit decision. The thinking: ‘If I get a contaminated letter, I’ll die. It isn’t a big hassle to don a mask and gloves while the contamination threat continues, and it eliminates my temporary fear, which is real though irrational’.

Spending a discretionary dollar on a lottery ticket with odds of 80 million to one involves a similar decision. The thinking: ‘I’m not in desperate financial straits, but it’s pleasant to think of the good life and all the altruistic things I could do with the payoff. I don’t expect to win, but it only costs a dollar to buy a fantasy I can only have by buying a ticket’.

So although we typically consider ourselves rationally-driven, our emotions strongly bias many of our decisions. The terrorists understand this, and have thus far been able to wage a successful emotional war against the US with much less funding and personnel than a traditional war would require.

It’s not unusual for people to be fearful of such generally safe things as snakes, elevators, and airplanes. In recent weeks, folks have driven hundreds of miles instead of flying even though driving requires greater effort, and the risk of an accident is much higher.

Thus far, four people have died of anthrax, which initially resembles flu, but their high profile deaths have sparked a much greater desire for flu shots than last year, when some 20,000 died of flu. Similarly, many people only buy lottery tickets when the payoff reaches $100 million or so, even though the odds of winning don’t improve at all with an increased payoff.

Last month’s column introduced the idea that our emotions powerfully affect the decisions we make. Far more fibers project from our brain’s emotional centers into the rational centers than the reverse. That wouldn’t be the case if our emotions were biologically unimportant to decision-making. Our challenge: be cautious about a new kind of danger that we don’t yet understand, but don’t allow fear to hold us in extended hostage to a very slight probability of danger.

Next month’s column will focus on how mass media help to distort our ability to rationally assess the probabilities of the potential risks and benefits that we confront.

In the meantime, you might want to read Larry Gonnick and Woollcott Smith’s delightfully informative The Cartoon Guide to Statistics (1993, Harper/Perennial) — an excellent non-technical explanation of statistical probability.