An Answer Page for Exercise 1

Exercise 1

Odds and probability are just two different ways of measuring the same thing.
Can you think of other situations where we sometimes measure or view the same concept in different ways ?


Here are a few examples. You can probably think of some better ones.

  Math and Physics
    The size of an angle can be measured in either degrees or radians.
    The slant of a line can be indicated by its slope or by
the angle whose tangent is the slope.
  Astronomy
    The passage of time can be measured in sideral or solar days
  Chemistry
    The concentration of a chemical solution can be measured in various ways.
For example, molarity Vs. molality:
        molarity = moles of solute per liter of solution
molality = moles of solute per kilogram of solvent
  Psychology
    There are various types of IQ tests for estimating human intelligence
 
  Of course, measurements can be made in metric, English, or other units.
    Munitions sizes:     9 mm bullet
38 caliber bullet
12 gauge shotgun shell
    Distance:   A race track could be measured in meters, furlongs, or miles.
    Power :   What is the horsepower of a 100 W light bulb ?
( Fact:   1 hp   =   746 watts   =   about 3/4 kilowatt )
    Temperature :   The formula   F   =   ( 9/5 ) C   +   32   can be used to
convert between Fahrenheit and Celsius temperatures.
    Area :   A cowboy could indicate the size of his ranch by saying
that it is   as big as so many football fields .

Some Related Issues

  Why do we usually define a right angle to be 90 degrees instead of 100 degrees ?
( Should a full circle have 400 degrees ?   Where did the "magic number" 360 come from ? )
  Are hawks "more intelligent" than eagles ?
  How would you measure literary merit ?   Is Macbeth as good as Hamlet ?
  How do you measure the quality of a wine or the safety and efficacy of a drug ?