How Are Sharks Less Dangerous than Vending Machines? An Exercise in Conditional Risk
Did you know that vending machines, not a major danger in most of our minds, are twice as likely to kill you as a shark? I heard this statistic at the new shark-and-ray touch tank of the New England Aquarium, which I try to visit weekly with my daughters. You stand at a large, shallow tank with plexiglass walls and can lay your hand in the water, gently feeling the sharks and sting rays swimming by.
The aquarium probably wants to convince visitors that sharks are not the fierce predators of Jaws fame, and thereby help protect sharks from hunting and extinction. Although I could admire this motive, the comparison always surprised me. My number sense complained that sharks simply must be more dangerous than vending machines.
However, upon looking up the risks, I found that the comparison was correct. The yearly risk (in the United States) of dying from a shark attack is roughly 1 in 250 million. In contrast, the yearly risk of dying from a vending machine accident is roughly 1 in 112 million. The vending machine is indeed roughly twice as lethal as the shark!
Why then was I still troubled by the comparison? Maybe my number sense needed a tune up, and I should just accept the statistical facts of life. I then started thinking about it using the method of easy cases.