## Fairness

Dies and Coins

People have been making decisions on the base of a coin toss, die roll, or other random drawing for many years. Why would they do such an insane thing? Why do people let a piece of metal (a coin) or a piece of plastic (dice) make a decisions in their lives? It is because they believe that these things are fair. Generally, in this context, fairness is defined as having an equal probability of obtaining any of the outcomes. So in a coin, there is an equal possibility of getting a head as a tail. Both have 1/2 chance of being obtained. If you do several tosses the number of heads and tails should be roughly the same. Put in different numbers for rolls down below and see what you get for heads and tails. They should be fairly close.
Lottery systems

In a military draft, the selection of candidates depends upon chance outcomes like a lottery. For example, during World War II, each man in each selective service district was assigned a number between 1 and 9000. The numbers were placed in identical capsules and were drawn one at a time from a larger container until all were removed. The order determined the order in which men were drafted. The table below shows the frequency showing the first 50 numbers drawn.

Does this draft look like it's fair? Why or why not? Look at the following graph. Anything new you can say from the graph?
Would you like to take your chances for being drafted in this lottery?
What if you had the number 1032 which is in interval 2?
What if you had the number 6212?
Remember that 6212 is in interval 7, but also remember that this the result of only 50 rolls.
Who knows what could happen in the next 50.
How would this impact our previous definition of fairness?

Final Words
Is Lucy being fair to Charlie Brown? She never lets him kick the ball. If she was being fair she would sometimes give him a chance, maybe half the time? He never learns.

When you want something to be fair you want each outcome to have an equal chance of occuring. Charlie Brown wishes that he would get just one shot in a hundred at kicking the football, but to you fairness should mean that everything should have an equal probability of occurring. Is it safe to say that you expect the outcomes to be equal? If you agree that our perception of fairness has to do with our expectations then we are ready to proceed to the next section.
Expectation