Using "expected value" to determine the value of information. Examples: Without information, should we drill for oil or not? With geological information, should we drill or not?

Even the most casual observers note the changes in the phase of the Moon as it goes from crescent to half to full and back again with a "monthly" cycle. (See Glenn Simonelli's PUMAS submission "Modeling the motions of the Earth, Sun and Moon" [PUMAS Example 03_10_04_1].) Their observations, or what is "common knowledge", lead them to believe the Moon does loops around the Earth. But is this true?

This simple example shows how algebra can be useful in the real world: Should Grandpa start receiving his Social Security Benefits at age 62 or should he wait until age 65?