COMPLEMENT OF AN EVENTDefinition: The complement of an event A is the set of alloutcomes in the sample space that are not included in theoutcomes of event A . The complement of event A isrepresented byRule: Given the probability of an event, the probability of itscomplement can be found by subtracting the given probabilityfrom 1 . P( )= 1 - P(A)
MUTUALLY EXCLUSIVE EVENTSDefinition: Two events are mutually exclusive if they cannotoccur at the same time (i.e., they have no outcomes incommon).
ADDITION RULESAddition Rule 1: When two events, A and B, are mutuallyexclusive, the probability that A or B will occur is the sum ofthe probability of each event.P(A or B) = P(A) + P(B)Addition Rule 2: When two events, A and B, are non -mutuallyexclusive, the probability that A or B will occur is: P(A or B)= P(A) + P(B) - P(A and B)
INDEPENDENT EVENTSDefinition: Two events, A and B, are independent if the factthat A occurs does not af fect the probability of B occurring.Multiplication Rule 1: When two events, A and B, areindependent, the probability of both occurring is: P(A and B)= P(A) • P(B)
DEPENDENT EVENTSDefinition: Two events are dependent if the outcome oroccurrence of the first af fects the outcome or occurrence ofthe second so that the probability is changed.
CONDITIONAL PROBABILIT YDefinition: The conditional probability of an event B inrelationship to an event A is the probability that event Boccurs given that event A has already occurred. The notationfor conditional probability is P(B|A) [pronounced as Theprobability of event B given A].Multiplication Rule 2: When two events, A and B, aredependent, the probability of both occurring is: P(A and B) =P(A) • P(B|A)
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.