CHAPTER 4
The notion of a random experiment is critical before taking up the subject of probability.
Random experiment: A well-defined procedure with a well-defined outcome (generally with an
uncertain outcome).
Common examples: flip a coin, roll a single die, roll two dice, draw two a card at random from a
standard card deck
Challenge for probability: When an experiment is considered, how many possible outcomes are
There? An elementary outcome is one which cannot be broken down further. So, if a single die is
rolled, the elementary outcomes are the numbers: 1, 2, 3, 4, 5, 6.
Note: you might be interested in classifying outcomes broadly such as “roll a even number,”
“number is greater than 2,” or “number is less than 5.” But all these outcomes are not
elementary, because they are comprised of more than one elementary outcome. For example, the
outcome: “roll an even number” is actually made up of outcomes 2, 4, and 6.
Before we tackle probability, we will consider the case when experiments are made up of a
sequency of several steps.
Examples: Roll two dice (die A and die B) – even if the dice are rolled simultaneously, the overall
outcome is made up of a pair of numbers, such as (a,b) = (1, 3) where die A = 1 and die B=3.
Or, flip 3 coins. Or draw 2 cards at random from a deck.
Let’s talk about a general method for counting the number of possible outcomes when there are
several steps in an overall experiment. Important: the outcome is considered to be the entire
sequence of outcomes at all steps in the experiment.
Suppose we flip a coin twice. The possible sequences of outcomes can be illustrated by a chain:
HH, TT, HT, TH (notice that HT is a different sequence than TH)
Notice that the total number of possible chains is 2*2=4 (2 outcomes are possible at each step in
the chain)
