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Probability
PART 6
The Basics
 Definition 1: An experiment is an occurrence with a
result that is uncertain before the experiment takes
place.
 Definition 2: The set of all possible outcomes is
called the sample space for the experiment.
 Definition 3: Given a sample space S, an event E is a
subset of S. The outcomes in E are called favorable
outcomes.
 Definition 4: The complement of an event E is the set
of outcomes not in E.
 Definition 5: The Law of Large Numbers states that
in order for an empirical probability to be close to
the value of the theoretical probability, you must
conduct the experiment a large number of times.
Probability Distributions
The probability of every element in the sample
space must be between 0 and 1, inclusive.
2. If we add the probabilities of every element in the
sample space, we must get 1.
3. If you have an event E that is a subset of your
sample space S, then we can add the probabilities
of all possible results in E to get the probability of E
itself.
1.
Addition Principle
 When presented with n different alternatives, each
with a certain number of outcomes, then you simply
add the outcomes to arrive at the total number of
alternatives.
 Example: Our family would like to go somewhere
this weekend. There are 5 museums, 3 movie
theaters, and 15 parks we could go to. If we are going
only one place, we have 5 + 3 + 15 = 23 alternatives.
Multiplication Principle
 When presented with a sequence of n choices, each
with a certain number of outcomes, then you
multiply the outcomes to arrive at the total number
of choices.
 Example: While at Baskin-Robbins I am building my
own ice cream treat. I first have to choose cone,
waffle cone, waffle bowl, or regular bowl. I then
choose the base flavor and finally choose the second
flavor. There are 4x31x31=3844 choices for a 2-scoop
ice cream treat.
Tips and Hints
 When looking at license plates, you have a sequence
of choices.
 These choices include ten numbers for the digits
place and twenty-six letters for the alphabet
characters.