Probability is the science of measuring the likelihood that an event will occur.
An Experiment is a controlled operation that yields a set of results.
Flipping a coin and identifying the side that is visible.
Selecting an item from a set of items (deck of cards for example)
Rolling a die and observing the number that is visible.
The outcomes of an experiment is the set of all possible results.
Flipping a coin, this is either "heads" or "tails"
Selecting a card we can define the following sets of outcomes
Color - red or black
Value A,2,3,4,5,6,7,8,9,10,J,Q,K
Suite: Diamond, Spade, Club, Heart
Picture (J,Q,K) or not
Plus others.
For a die, it is usually a number
1-6 for a standard die
Other values for other types of dice.
An event is a subset of the outcomes of an experiment.
Flip a coin and heads occurs.
Select a card from the deck and it is the queen of diamonds
Select a card from the deck and it is a queen.
Select a card from the deck and it is ...
Roll a die and the result is even, greater than 5, ...
In empirical probability the probability of an event is determined by conducting the event a number of times
Number of times E occurs
P(E) = --------------------------
Number of experiments done
Do problem 17- on page 642
The law of large numbers states that probability statements apply in practice to a large number of trials, not a single trial. It is the relative frequency over the long run that is accurately predictable, not individual events or precise totals.
Outcomes are equally likely both have the same chance of occurring.
Each number on a fair die is equally likely.
Each side of a fair coin is equally likely.
Each card is equally likely, but face vs number cards are not equally likely.
In theoretical probability the probability of an event is calculated using
Outcomes in E
P(E) = --------------
Total Outcomes
if all outcomes are equally likely.
P(E) = 0 if and only if E cannot occur.
P(E) = 1 if and only if E must occur.
0 ≤ P(E) ≤ 1
The sum of the probability of all outcomes of an experiment is 1.