Download Addition Rule for disjoint events

Chapter 6 Vocabulary
Random- We call a phenomenon if individual outcomes are uncertain but there is nonetheless a regular
distribution of outcomes in a large number of repetitions.
Probability- outcome of a random phenomenon is the proportion of times the outcome would occur in a very
long series of repetitions.
Sample Space S- The sample space S of a random phenomenon is the set of all possible outcomes.
Tree diagram- A way to list possible outcomes in an experiment that resembles the branches of a tree.
Multiplication Principle- If you can do one task in a number of ways and a second task b number of ways,
then both tasks can be done in a x b number of ways.
With replacement- When selecting object from a collection of distinct objects from a collection of distinct
choices, if you replace the selection back into the objects then you a selecting with replacement.
Without replacement- When selecting object from a collection of distinct objects from a collection of distinct
choices, if you do not replace the selection back into the objects then you a selecting without replacement.
Event- An event is an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of
the sample space.
Probability Rules
Rule 1. The probability, P(A), of any event A satisfies 0  P( A)  1 .
Rule 2. If S is the sample space in a probability model, then P(S) = 1.
Rule 3. The complement of any event A is the event that A does not occur. Written as Ac . The complement
rule states that
P( Ac ) = 1 – P(A)
Rule 4. Two events A and B are disjoint if they have no outcomes in common and so can never occur
simultaneously. If A and B are disjoint,
P(A or B) = P(A) + P(B)
This is the addition rule for disjoint events.
Venn diagram- A helpful way to remind ourselves of the complement and disjoint events. Shows the sample
space S as a rectangular area and events as areas with S.
Probabilities in a Finite Sample Space
Assign a probability to each individual outcome. The probabilities must be number between 0 and 1 and must
have sum 1.
The probability of any event is the sum of the probabilities of the outcomes making up the event.
Equally Likely Outcomes- If a random phenomenon has k possible outcomes, all equally likely, then each
individual outcome has probability 1/k. The probability of any event A is
count of outcomes in A
P( A) 
count of outcomes in S
The Multiplication Rule for Independent Events
Rule 5. Two events A and B are independent if knowing that one occurs does not change the probability that
the other occurs. If A and B are independent,
P(A and B) = P(A)P(B)
This is the multiplication rule for independent events.
Union- The union of any collection of events is the event that at least one of the collection occurs.
Addition Rule for disjoint events
If events A, B, and C are disjoint in the sense than no two have any outcomes in common, then
P(one or more of A, B, C) = P(A) + P(B) + P(C)
This rule extends to any number of disjoint events.
General Addition Rule for Unions of Two Events
For any two events A and B,
P(A or B) = P(A) + P(B) – P(A and B)
Joint event- The simultaneous occurrence of two events.
Joint probability- The probability of a joint event.
Conditional probability- the probability of one event under the condition that we know another event.
General Multiplication Rule
The joint probability that both of two events A and B happen together can be found by
P(A and B) = P( A) P( B A) . P( B A) is the conditional probability that B occurs given the information that A
occurs.
Definition of Conditional Probability
When P(A) > 0, the conditional probability of B given A is
P(A and B)
P( B A) 
P( A)
intersection- The intersection of any collection of events is the event that all of the events occur.
Independent events- The events A and B that both have positive probability are independent if
P( B A)  P( B)