One of my favorite examples of something that doesn't add up according to common sense comes from the field of statistics.
Say you're taking a survey that consists of a single question, the answer to which can only be yes or no. Assuming you're able to select people randomly, how many people would you have to survey to have an assurance of 95% that your result is correct within 5% for all the people in:
- The state of Wyoming (population 453,588)
- The state of South Carolina (population 4,012,012)
- The state of California (population 33,871,648)
- The United States (population 281,421,906)
The answer? Actually, I've forgotten the exactly correct answer, but it's a little more than 1700 people, and it's the same no matter what the population (as long as the population is significantly larger than 1700). Imagine that! It makes no difference whether you're surveying a population of 10 million or 10 billion, you only need to survey a little more than 1700 people!
If anyone has a common sense explanation for why that should be the case, I'm listening!
--Percy
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