• Disjoint Event
Two events, A and B, are disjoint if they do not have any
common outcomes.
• Intersection of Two Event
The intersection of A and B consists of outcomes that are in
both A and B, denoted by A∩B.
• Union of Two Event
The union of A and B consists of outcomes that are in A or
B, denoted by A∪B.
• Addition Rule
For the union of two events,
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
If the events are disjoint, then P(A ∩ B)=0, so
P(A ∪ B) = P(A) + P(B).
Example:
Consider the reading habits of the 1070 class. If we know that
30% of the class students read USA Today daily, 40% read Salt
Lake Tribune daily and 10% read both of them daily, what is the
percentage of the 1070 class students who do not read these two
newspapers daily?
• Independent Trials
Different trials of a random phenomenon are independent if
the outcome of any one trial is not affected by the outcome of
any other trial.
• Multiplication Rule
For the intersection of two independent events, A and B,
P(A ∩ B) = P(A) × P(B).
Caution: events often are not independent.
Rules for Finding Probabilities
• The probability of each individual outcome is between 0 and
1, and the total of all the individual probabilities equals 1.
The probability of an event is the sum of the probabilities of
the individual outcomes in that event.
• For an event A and its complement Ac (not in A),
P(Ac ) = 1 − P(A).
• The union of two events (that is, A occurs or B occurs or
both) has
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
• When A and B are independent, the intersection of two
events has
P(A ∩ B) = P(A) × P(B).
• Two events A and B are disjoint when they have no common
elements. Then
P(A ∩ B) = 0, and thus P(A ∪ B) = P(A) + P(B).