Selections from Deborah Bennett's book, Randomness
The headline of a 1990 New York Times article reads as follows: "1-in-a-Trillion Coincidence, You Say? Not Really, Experts Find." The article goes on to report a seemingly unbelievable coincidence about a woman who won the New Jersey lottery twice within four months, a feat originally reported as a 1 in 17 trillion long shot. Research on coincidences by two Harvard statisticians revealed, however, that the odds of such an event happening to someone somewhere in the United States were more like 1 in 30--not that amazing after all. They explain that this is an example of the law of very large numbers: "With a large enough sample, any outrageous thing is likely to happen." Out of the millions upon millions of people who regularly purchase lottery tickets in the United States, it is not unreasonable that someone should at some point hit the lottery twice.
--page 72, Randomness
Another article in the New York Times...regarding the tragic TWA Flight 800 crash...reported that "more than once, senior crash investigators have tried to end the speculation by ranking the possibility of friendly fire at about the same level as that a meteorite destroyed the jet." In a letter to the editor..., Charles Hailey and David Helfand wrote: "The odds of a meteor striking TWA Flight 800 or any other single airline flight are indeed small. However, the relevant calculation is not the likelihood of any particular aircraft being hit, but the probability that one commercial airliner over the last 30 years of high-volume air travel would be struck by an incoming meteor with sufficient energy to cripple the plane or cause an explosion." Noting that 3000 meteors with the requisite mass hit the earth every day, and that 50,000 commercial airline flights occur worldwide each day; and assuming an average flight time of two hours, which translates into more than 3500 planes in the air at any moment; and calculating that these planes would cover approximately two-billionths of the earth's surface, the authors conclude that, in over 30 years of air travel, the probability that a commercial flight would have been hit by meteoric impact sufficient to crash the plane is 1 in 10.
--page 73, Randomness
If a test to detect a disease whose prevalence is one in a thousand has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person's symptoms or signs?
(try computing this yourself; click for answer)
link to more information about Deborah Bennett's Randomness
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