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Unit 3 Chapter 3 - Definitions
Probability is a numerical measure between 0 and 1 that describes the likelihood that an event will
occur.
0 P(A)  1
never negative or over 1
Notation: P(A) is read as “the probability of event A happening”
Event: an event is a collection or set of one or more simple event in the sample space.
Sample space: this is the list of all possible outcomes from a random experiment.
Pr obability of an event 
Number of outcomes favorable to event
Total number of outcomes
The complement of a event A is the event that A does not occur, A ’
1) P(A) + P(A’ ) = 1
2) P(A ’) = 1 – P(A) and P(A) = 1 – P(A ’ )
Two events are independent if the occurrence or nonoccurrence of one does not change the probability
that the other will occur.
If events A and B are independent, then P(A and B) = P(A)  P(B).
Two events are dependent if the occurrence or nonoccurrence of one does change the probability that
the other will occur.
For dependent events:
P(A and B) = P(A) P(B| A)
P(B | A) is called a conditional probability because it depends A occurring first.
“the probability that event B happens, given that event A has already occurred”
Two events are mutually exclusive or disjoint if they cannot occur at the same time. If P(A and B) = 0,
the events A and B are mutually exclusive.
Addition rule of mutually exclusive events A and B:
P(A or B) = P(A) + P(B)
Addition rule for not mutually exclusive events A and B:
P(A or B) = P(A) + P(B) – P(A and B)
Counting techniques
Creating groups of characters – this is really an example where the multiplication rule can be applied.
Think of the experiment where you are picking numbers out of a hat to fill each place value.
How many groups can be created from
1) 4 single digits (recall there are 10 single digits 0 – 9)
10101010 = 10,000 groups
2) 4 single digit without replacement
10987 = 5040 groups
3) 3 single digits followed by 2 letters
(recall there are 26 letters)
1010102626 = 676,000 groups
Factorial notation
For a counting number n
0! = 1  Be very careful with this one!!
1! = 1
n! = n(n – 1)(n – 2)…1
Example:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Counting rule for permutations
(Use this rule when it MATTERS which order the objects are in)
The number of ways to arrange in order n distinct objects, take then r at a time is
n Pr 
n!
(n  r )!
where n and r are whole numbers and n  r .
Counting rule for combinations
(Use this rule when it DOES NOT MATTER in which order the objects are placed)
The number combinations of n object take r at a time is
Cn , r  nCr 
n!
r!(n  r )!
where n and r are whole numbers and n  r .