Probability

In the last 10 to 15 years PROBABILITY has shown up a lot more at the elementary
school level.   As a matter of fact it happens in 6th grade for most and in some places
even earlier.   It did for 2 reasons:

• It is a great example of a fraction in life.
• It is a fine way to look at percents.

For many of us as parents, when these questions come home we may be at a loss to 

help little Johnny or Mia.  But we can help if we just think of that coin being tossed 

in the air.  There are a total of 2 possibilities: HEADS OR TAILS.  However, there

is only one winner.  

The Probability of of getting heads or tails is ½, or 50% or .50

So we can think of Probability as

     P(EVENT OCCURRING)  =
                     Number of favorable outcomes 
                               Total number of outcomes

We can write probabilities as a 

• FRACTION 
• DECIMAL
• PERCENT

So lets ask some questions:

Example: You have a box containing 10 marbles.   3 are RED,
                 4 are YELLOW,  2 are GREEN, and one in WHITE.
                 They are all the same size and feel the same.  If you
                 reach in and randomly draw one out of the box, what
                 is the Probability that it will be YELLOW?

             4 Favorable and 10 Total

            ∴ 4/10 = 2/5   You have 2 chances out of 5.


Example: Given the same box and marbles you have above, what is
                the percentage chance of picking a GREEN marble?

            2 Favorable and 10 Total

            ∴ 2/10 = 1/5    1/5 = .20 = 20%

            You have a 20% chance of drawing out a GREEN marble.

What I have just discussed with you is called THEORETICAL PROBABILITY
because it is based on knowing all of the outcomes that are equally likely.




This needs to be separated from EXPERIMENTAL PROBABILITY which is
based on repeated trials of an experiment.

  EXPERIMENTAL PROBABILITY OF AN EVENT

                          =  NUMBER OF SUCCESSES 
                                NUMBER OF TRIALS


 Example:  You roll a six sided die. The chance that any one side
                  comes up is equally likely.  You roll the die 40 times
                  and note all the results.  What is the Experimental
                  Probability of getting an odd number on any role?

                    Here are your results:

     RESULT               1        2         3         4        5         6
TIMES ROLED         6        7         7        5       10         5

                      23 out of 40 are odd!   57.5% are odd
               Our P(odd) is 57.5% (Experimental)


               20/40 or 50% are odd  is the 
               Theoretical Probability.


This is only beginning of a long discussion.  In my next Blog I will discuss
the ideas of independent and dependent events.