Theoretical Probability

Discussion

We generally don't work with empirical probability.
From now on, when we state probability, we mean theoretical probability.
If each outcome of an experiment has the same chance of occurring as every other outcome, then the events are said to be equally likely
In this case, the probability of an event E can be computed by

        number of events favorable to E
P(E) =  -------------------------------
           Total number of events

Example 1

A 8 sided dice is to be tossed.  
Find the probability of rolling
   There are 8 different outcomes, each is equally likely.
   A.  An 8
        There is one way to roll an 8

	P(E) = 1/8  = 12.5%
   B.  A 3
        Again there is one way to roll a 3.

	P(E) = 1/8 = 12.5%

   C.  A number less than 2
        You can roll either a 1 or a 2.

	P(E) = 2/8 = 1/4 = .25 or 25%

   D.  An even number
        You could roll a 2, 4, 6, or 8

	P(E) = 4/8  = 1/2 = .5 or 50%

   E. A 12
      
        No events generate a 12, so

	P(E) = 0/8 = 0 or 0%

   F.  A number between 1 and 8
        This event is generated 8 ways, 1,2,3,4,5,6,7,8

	P(E) = 8/1 = 1 or 100%

   G.  A number other than 8
        This event is generated 7 ways: 1,2,3,4,5,6,7

	P(E) = 7/8 = 87.5%
	(Note as below this is 1-P(8), or 1-1/8)

Note:
- The probability of an event that can not occur is 0.
- The probability of an event that must occur is 1.
- The probability of an event that can occur is between 1 and 0.
- No probability is higher than 1 or less than 0.
- The probability of an event occurring is one minus the probability of an event not occurring.

Homework

Please do 17-72 odds. p 668

Theoretical Probability

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