Some phenomena have predictable outcomes: drop a coin from known height and the time it takes to fall can be predicted from basic physics. Except for a rather small measurement error, the outcome is certain. If we toss the coin, on the other hand, we cannot predict whether it will show heads or tails. The outcome is uncertain. Yet coin tossing is not haphazard. If we make a large number of tosses, the proportion of heads will be very close to one-half....
Phenomena having uncertain individual outcomes but a regular pattern of outcomes in many repetitions are called random. "Random" is not a synonym for "haphazard" but a description of a kind of order different from the deterministic one that is popularly associated with science and mathematics. Probability is the branch of mathematics that describes randomness....
Uncertainty is of course a pervasive aspect of all human experience; it is the order in uncertainty that is hard to observe.... Psychologists have shown that our intuition of chance profoundly contradicts the laws of probability that describe actual random behavior. This incorrect understanding is very difficult to correct by formal instruction....
One goal of instruction about probability is to help students understand that chance variation rather than deterministic causation explains many aspects of the world.
Suppose that a basketball player over a long season has made 70% of her free throws. At the end of a tournament game she attempts five free throws and makes only two. "Nervousness," say the fans. But this causal explanation need not be correct. A player having a probability of 0.7 of making each shot has a probability of about 0.16 of missing three or more of five shots. Such a performance can easily be simply chance variation.
Some understanding of probability enables us to consider the role of chance rather than seek a specific cause, oftentimes spurious, for every occurrence.
(excerpts from David S. Moore's "Uncertainty," a chapter in On the Shoulders of Giants: New Approaches to Numeracy, edited by Lynn Arthur Steen.)
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