A random process is a situation that can be repeated and for which the set of possible outcomes is known.
There is a predictible pattern that appears with many repetitions.
The collection of all possible outcomes of a random process is called the sample space.
Each element in the sample space is an outcome.
An event is any collection of outcomes from the sample space of a random process. Events are typically denoted with a capital letter.
Many questions involve choosing one or more items from a collection of items. If we choose more than one item, we can select with replacement or without replacement, where we can return or not return the item.
The probability that an event will occur is the proportion
of time the event occurs over the long run, or the relative frequency
with which the event occurs if we repeat the random process over and
over again.
P(A) = # of times A occurs / number of times process is repeated
When the outcomes in the sample space are equally likely, we can determine
the probability of an event, A, by:
P(A) = # of outcomes in A/ number of outcomes in sample space
This method is called the counting method.
1. 0 <= P(A) <= 1, the probability of an event is always
a number between 0 and 1, inclusive.
2. P(S) = 1, the sum of all the probabilities in the sample
space is 1.
3. If a random process has n equally likely outcomes,
the probability of each is 1/n.
4. P(A) = 1 - P(not A), an event A either
occurs or not, and P(not A)= 1 - P(A).
5. If A and B are events with no outcomes
in common, P(A or B) = P(A) + P(B). Events with no outcomes
in common are called disjoint or mutually exclusive.