Math 141, Sem. I, 1998-99 (R.A. Brualdi)
Handout 20 (November 16, 1998)
Topic: Probability 


There are two kinds of probability: statistical probability and
mathematical probability.

Example: (stat. prob) Probability of rain today is 30% (or .30).  Such a
probability comes from looking at the atmospheric conditions, using
previous knowledge from past experience, ... and then making an "informed
guess." 

Example: (math. prob.) Probability that a coin comes up Heads when tossed
is 1/2. This assigned probability is based on a mathematical model that we
construct: there are two possible outcomes (H - heads and T - tails), and
assuming the coin is `fair'  each of H and T is equally likely. So each
has "1 out of two chances" of occurring if a coin is tossed.

   Prob (Heads) = 1/2
   Prob (Tails) = 1/2.

If a coin is tossed a large number of times, you expect that about half
H's and half T's (even though a particular 100 tosses might result in 57
H's and 43 T's; it even might result in 100 H's and 0 T's!). 


Some language: 

*sample space S*: set of all possible outcomes of an experiment. 
*event E*: some of the outcomes of an experiment (a subset of the sample
         space)
  events are usually given descriptively.

Example. Experiment: Toss a die.

   sample space S is: 1, 2, 3, 4, 5, 6 (number of dots on top)
   event E: number of dots is at least 4
            As a subset of the sample space E is 4, 5, 6.

Examples to be discussed in class: Cards drawn from 1 52 deck.

PROBLEM: Suppose that a newborn child has an equal chance of being a boy
or a girl. (statistical probabilities would tell us that this is not quite
correct). A couple decides to have 4 children. What is more probable
(least probable):

 4 children of the same sex,
 2 of each sex,
 3 of one sex and 1 of another?