Misapplications Reviews: Mea Culpa.

The article presents a commentary on the mathematical errors made in discussing about risk assessment and marketing. It analyzes the bias in computing for the chance that a given Air Canada flight will end catastrophically and finds error concerning the purchase of cat food. Perhaps the broader difficulty is that one often faces optimization problems without consciously realizing it. Buying a small box with a coupon increases the number of purchases that must be made without any discount. Hence the overall price per ounce actually goes up, except of course when the number of coupons approaches the number of boxes needed. For any enterprise viewed as potentially hazardous--whether it involves nuclear power plants, liquid natural gas tankers, or a new, low-fare airline--attention will be paid when the first accident strikes to the number of operations until the disaster. It will be most tempting to use the reciprocal of that quantity as an estimate of the future rate of accidents. Over time, the observed ratio of accidents to flights will oscillate randomly around P: it will jump up just after a crash, gradually diminish as succeeding months pass without incident, and then jump up again at the time of the next accident.