An experiment is a controlled operation that yields a set of results.
Just like probability.
Note the use of set.
An outcome is one of the possible results of an experiment.
An event is a set of outcomes.
I roll a six sided die and observe the number on top. I note when the number is even.
The experiment is rolling the die
The outcomes are {1,2,3,4,5,6}
The event I am interested is when the result is in {2,4,6}
I flip a coin and check to see if it is heads
The experiment is flipping a coin
The outcomes are either heads or tails.
The event is that heads appears.
I select two card from a standard deck of cards and look to see if they have the same color.
The Experiment is selecting two cards
The outcomes are {RR, RB, BR, BB}
The event is the cards match. {RR, BB}
If we calculate the probability based on experimentation we calculate Empirical Probability
number of times event E has occurred
P(E) = _______________________________________________________
total number of times the experiment has been performed
Do problem 19 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.
Equally Likely outcomes are events that have the same chance of occurring.
Theoretical probability is based on examining the experiment, events and outcomes.
$P(E) = \frac{n(E)}{n(U)}$
Some Facts:
0 ≤ P(E) ≤ 1 for all E.
The sum of all probabilities of all possible outcomes of an experiment is 1.