An experiment is a controlled operation that yields a set of results.
Outcomes are the possible results of an experiment.
An event is a subset of the outcomes of an experiment.
Empirical Probability is determined by conducting an experiment a number of times, counting the number of successes and using the following formula
Number of times E has occurred
P(E) = --------------------------------------------------
Total number of times the experiment was performed
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 ore precise totals.
Example 1: Roll a standard die
The experiment is to roll a die and look at the number on the top.
The outcomes are : 1, 2, 3, 4, 5, 6
Some events are
The result is even
The result is four
The result is greater than 2
Example: toss a fair coin
The experiment is to toss a coin and look at the top face showing
The outcomes are heads or tails
Some events are
The result is heads
The result is tails
Example: Draw a card from a standard deck
Draw a card and look at it
There are a 52 outcomes, Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King of Diamonds, Spades, Hearts and Clubs.
26 cards are red and 26 cards are black
12 cards are face cards (an ace is not a face card)
Many events:
The jack of diamonds is drawn
A face card is drawn
A red card is drawn
Example: Roll two standard dice
The outcomes are 1,1, 1,2 1,3, 1,4, 1,5 1,6 2,1, 2,2 ... 6,6
Events are many
The sum is 5
Both die are even
The sum is odd
Example: Of 60 people at a cash register , 13 had blond hair, 15 had black, 25 had brown and 7 had red hair. Find the empirical probability that the next person to come to the cash register has black hair.