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Story 1
1. An airplane takes off from Los Angeles, on the way to New York, where it is expected to arrive 5 hours later. However, after the first hour in the air, the captain makes an announcement: “Hello. This is your captain speaking. I’m afraid one of the four engines has broken down. We can still get to New York with three engines, but it will take us 7 hours. I apologize for the inconvenience.” After the second hour in the air, the captain makes another announcement: “This is your captain speaking. I’m afraid another engine has broken down. We can still get to New York with two engines, but it will take us 10 hours. I apologize for the inconvenience.” After the third hour in the air, the captain makes another announcement: “I’m afraid another engine has broken down. We can still get to New York with one engine, but it will take us 18 hours. I apologize for the inconvenience.” On board are two statisticians. One of them turns to the other and says “I hope the other engine doesn't break down, or we’ll be up here for ever!”
Story 1
2. A student of statistics is accompanying his statistics professor in his car. The student is puzzled, since the professor never stops for red lights, but drives speedily through every intersection. When the student asks the professor about this, he replies: “Intersections have extremely high accident rates. Therefore I try to spend as little time in them as I can.”
The point about these two stories is not that the statisticians were wrong to make their assumptions, but that they were focusing on isolated factors, without looking at the overall situation. In the first story, we can see that the amount of time spent in the air was inversely proportional to the number of engines (figure 1, below), and that this time was increasing logarithmically as the number of engines decreased. On the basis of these facts, it would seem correct to infer that when the number of engines was further reduced, then the time in the air would approach infinity, so that the plane would never come down. Common sense, on the other hand, tells us that the plane would in fact crash, since there would be no means of propulsion. Thus, if we added the speed of the plane to the graph in figure 1, this would show us that the plane’s velocity was decreasing along with the number of engines, though the graph would still not allow us to consider factors such as flying height, wind speed, air temperature, ground conditions, and panic-produced human errors.
