2. COMPLEMENT OF AN EVENT
Definition: The complement of an event A is the set of all
outcomes in the sample space that are not included in the
outcomes of event A . The complement of event A is
represented by
Rule: Given the probability of an event, the probability of its
complement can be found by subtracting the given probability
from 1 . P( )= 1 - P(A)
3. MUTUALLY EXCLUSIVE EVENTS
Definition: Two events are mutually exclusive if they cannot
occur at the same time (i.e., they have no outcomes in
common).
4. ADDITION RULES
Addition Rule 1: When two events, A and B, are mutually
exclusive, the probability that A or B will occur is the sum of
the probability of each event.
P(A or B) = P(A) + P(B)
Addition Rule 2: When two events, A and B, are non -mutually
exclusive, the probability that A or B will occur is: P(A or B)
= P(A) + P(B) - P(A and B)
5. INDEPENDENT EVENTS
Definition: Two events, A and B, are independent if the fact
that A occurs does not af fect the probability of B occurring.
Multiplication Rule 1: When two events, A and B, are
independent, the probability of both occurring is: P(A and B)
= P(A) • P(B)
6. DEPENDENT EVENTS
Definition: Two events are dependent if the outcome or
occurrence of the first af fects the outcome or occurrence of
the second so that the probability is changed.
7. CONDITIONAL PROBABILIT Y
Definition: The conditional probability of an event B in
relationship to an event A is the probability that event B
occurs given that event A has already occurred. The notation
for conditional probability is P(B|A) [pronounced as The
probability of event B given A].
Multiplication Rule 2: When two events, A and B, are
dependent, the probability of both occurring is: P(A and B) =
P(A) • P(B|A)
8. ARRANGEMENTS AND COMBINATIONS
Arrangement-ordering of items (also called Permutation).
Arrangements can be expressed using a tree diagram, which
shows all the possibilities
Combination-the number of ways of selecting B objects from A
objects. Choice in the order of the items does not matter
Fundamental Counting Principle - the number of possible ways
to get an outcome. The events are independent so the
outcomes are multiplied.
