© David Lippman
Creative Commons BY-SA
The probability of a specified event is the chance or likelihood that it will occur. There are
several ways of viewing probability. One would be experimental in nature, where we
repeatedly conduct an experiment. Suppose we flipped a coin over and over and over again
and it came up heads about half of the time; we would expect that in the future whenever we
flipped the coin it would turn up heads about half of the time. When a weather reporter says
“there is a 10% chance of rain tomorrow,” she is basing that on prior evidence; that out of all
days with similar weather patterns, it has rained on 1 out of 10 of those days.
Another view would be subjective in nature, in other words an educated guess. If someone
asked you the probability that the Seattle Mariners would win their next baseball game, it
would be impossible to conduct an experiment where the same two teams played each other
repeatedly, each time with the same starting lineup and starting pitchers, each starting at the
same time of day on the same field under the precisely the same conditions. Since there are
so many variables to take into account, someone familiar with baseball and with the two
teams involved might make an educated guess that there is a 75% chance they will win the
game; that is, if the same two teams were to play each other repeatedly under identical
conditions, the Mariners would win about three out of every four games. But this is just a
guess, with no way to verify its accuracy, and depending upon how educated the educated
guesser is, a subjective probability may not be worth very much.
We will return to the experimental and subjective probabilities from time to time, but in this
course we will mostly be concerned with theoretical probability, which is defined as
follows: Suppose there is a situation with n equally likely possible outcomes and that m of
those n outcomes correspond to a particular event; then the probability of that event is
If you roll a die, pick a card from deck of playing cards, or randomly select a person and
observe their hair color, we are executing an experiment or procedure. In probability, we
look at the likelihood of different outcomes. We begin with some terminology.
Events and Outcomes
The result of an experiment is called an outcome.
An event is any particular outcome or group of outcomes.
A simple event is an event that cannot be broken down further
The sample space is the set of all possible simple events.