The Probability Scale

We can make our probability claims more precise by using numbers. Sometimes we use percentages. For example, the weather bureau might say that there is a 75 percent chance of snow tomorrow. This can naturally be changed to a fraction: The probability is 3/4 that it will snow tomorrow. Finally, this fraction can be changed to a decimal expression: There is a 0.75 probability that it will snow tomorrow.

The probability scale has two end points: the absolute certainty that the event will occur and the absolute certainty that it will not occur. Because you cannot do better than absolute certainty, a probability can neither rise above 100 percent nor drop below 0 percent (neither above 1, nor below 0). (This should sound fairly obvious, but it is possible to become confused when combining percentages and fractions, as when Yogi Berra was supposed to have said that success is one-third talent and 75 percent hard work.) Of course, what we normally call probability claims usually fall between these two endpoints. For this reason, it sounds somewhat peculiar to say that there is a 100 percent chance of rain and just plain weird to say the chance of rain is 1 out of 1. Even so, these peculiar ways of speaking cause no proce- dural difficulties and rarely come up in practice.

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included Andrew Toney, noted around the league as being streak shooter. The authors found no evidence for streak shooting, not even for Andrew Toney. How would you go about deciding whether streak shooting exists or not? If, as Gilovich, Vallone, and Tversky have argued, belief phenomenon is a “cog- nitive illusion,” why do so many people, including most professional athletes, believe that it does exist?