Am I asking for trouble by visiting London after two terrorist attacks?
Should I buy a lottery ticket every week, or bank the money instead?
What are my chances of catching the deadly bird flu?
Every day, people across the globe are calculating the chances of good or bad outcomes in their lives. But, says a University of Toronto statistician, many people make decisions based on scanty information, half-truths or even superstitions.
"Knowing the rules of probability, randomness and uncertainty allows us to make better decisions and to understand the world around us more clearly," says Jeffrey Rosenthal in his new book Struck by Lightning: The Curious World of Probabilities.
Instead of leaving the results to fate, or shrugging off a rational approach as too much work, he says setting out the facts and calculating the probabilities can reduce stress and help people to lead less worrisome lives.
"As a young person I used to be nervous when flying," he says. "If there was turbulence I'd worry. But later I began to realize that there are a million flights in a year, and very, very few of them crash. In fact, it was incredibly unlikely that my plane would crash."
Rosenthal, a 37-year-old statistics professor at the University of Toronto, and sometime improv comedian, wrote his book after considering the extent chance affects our daily lives.
Chance, or randomness, is everywhere, he realized. And it's unavoidable even for the most cautious: those who take medication weigh the chance of cure against the risk of side effects. Hosts toss mental coins that it won't rain at their picnics. Engaged couples wonder if their marriages will succeed when so many fail. Job seekers gamble that lower-paying work will lead to a promotion later on.
Calculating success or failure, says Rosenthal, helps to separate unacceptable from acceptable risk, giving us more informed choices. A proposition few could quibble with.
But probability also has its controversial side. In an age when religious fundamentalism and belief in the paranormal are entering the mainstream, many people resist reducing what they believe are supernatural experiences to numbers on a page. There are bitter divisions between those who believe in a random universe in which man has free will, and those who feel life is pre-ordained, or directed by an other-worldly being.
"People have a built-in need to ascribe a moral force to the universe," Rosenthal explains. "When things happen, there has to be a reason, whether because of religion or superstition. It was like that in the past, and a lot of it survives today."
In the dim dawn of humanity, early man looked on natural occurrences as portents: storms, droughts, fires, crop failures were signs that he had displeased vengeful gods. Places, objects and animals were linked with evil events in legends that have endured for centuries.
"Even today there's no 13th floor in buildings," Rosenthal points out. "People don't like to walk under ladders. They avoid black cats."
Many people today, too, give coincidence special meaning. Receiving a phone call from someone they have just been thinking about seems telepathic, meeting a friend in a city far from home is "uncanny," and missing the train on the day of a crash is "fate."
But, says Rosenthal, when the odds on those events are calculated, they may be less outlandish than we believe.
"People often think there's no such thing as coincidence, because they don't like to think these things happen just by chance. It's important to understand them, not because we shouldn't be fascinated by chance, but because if you understand how things come up you'll be better prepared for them."
One of the problems, he says, is that people tend to use a "biased sampling approach," to events they experience, remembering only things that back up pre-determined ideas: if a red-headed child kicks his schoolmates, the next belligerent red-head may be seen as typical.
"That can lead to stereotyping," Rosenthal warns. "Because you feel that certain people do this or that, you've forgotten all the times when totally different people did the same things."
Similarly, he says, reading or viewing media reports can give a biased view of reality because the headlines give great importance to rare events, and what makes news is the exception and not the rule.
In the 1990s, Rosenthal says, he decided to challenge police views that crime was increasing by checking the figures. He found that "crime was actually decreasing during those years. But fear of crime wasn't."
Terrorism, too, has made people anticipate an attack at any time. "Anxiety medication (sales) went way up after 9/11, and many people said it changed the way they lived their lives. But as far as the chance of being killed randomly and horribly goes, things didn't change as much as people were led to believe."
"I believe in balancing the uncertainties we face. Some people do things at any cost. Others, if there's any risk at all, say they wouldn't think about it. I come down in the middle. I don't think about probability every minute, but when something comes up, I do the calculations to get a sense of things. It's a quick reality check."