Download Chapter 5 Addition rules for probability For mutually exclusive

Chapter 5
Addition rules for probability
For mutually exclusive events, the probabilities can simply be added together. If the events can
be co-occurring, you should subtract the probability of a co-occurring event which is otherwise
counted twice (once for each event).
(For more information, review Section 5.2)
Combinations rule
The number of combinations of n objects taken r at a time is the permutations divided by r
factorial where n and r are whole numbers and n is greater than or equal to r. Another commonly
used notation for c
Conditional probability
Conditional probability is the probability that a dependent event will occur given that another
event has occurred.
(For more information, review Section 5.2)
Dependent events
If events are dependent, the probability of one event depends upon the occurrence of the other
event.
(For more information, review Section 5.2)
Event
An event is a collection of one or more outcomes of a statistical experiment.
(For more information, review Section 5.1)
Factorial
For a number n, its factorial is the product of n with each of the positive counting numbers less
than n. By special definition, the factorial of zero is 1.
(For more information, review Section 5.3)
Independent events
Two events are independent if the occurrence or nonoccurrence of one does not change the
probability that the other will occur.
(For more information, review Section 5.2)
Law of large numbers
In the long run, as the sample size increases and increases, the relative frequencies of outcomes
get closer and closer to the theoretical (or actual) probability value.
(For more information, review Section 5.1)
Multiplication rule of counting
The total number of possible outcomes for a sequence of events is the product of the number of
possibilities for each event in the sequence.
(For more information, review Section 5.3)
Multiplication rules of probability (for independent and dependent events)
For independent events, the probabilities can simply be multiplied. For conditional events, the
probability of the independent event is multiplied by the conditional probability of the dependent
event.
(For more information, review Section 5.2)
Mutually exclusive events
Two events are mutually exclusive or disjoint if they cannot occur together. In particular, events
A and B are mutually exclusive if P(A and B) = 0.
(For more information, review Section 5.2)
Permutations rule
For a number of choices n and a number of choices r, The number of ways to arrange in order n
distinct objects, taking them r at a time, is n factorial divided by (n-r) factorial where n and r are
whole numbers and n is greater than or equal to r. Another commonly used notation for
permutations is nPr.
(For more information, review Section 5.3)
Probability of an event A, P(A)
Probability is a numerical measure between 0 and 1 that describes the likelihood that an event
will occur. Probabilities closer to 1 indicate that the event is more likely to occur. Probabilities
closer to 0 indicate that the event is less likely to occur. P(A), read "P of A," denotes the
probability of event A.
(For more information, review Section 5.1)
Relative frequency
The relative frequency of an event is its frequency divided by the number of total observations.
(For more information, review Section 5.1)
Sample space
The set of all simple events constitutes the sample space of an experiment.
(For more information, review Section 5.1)
Simple event
A simple event is one particular outcome of a statistical experiment.
(For more information, review Section 5.1)
Simple tally survey
A simple tally survey consists of questions to which the responses are recorded in the rows and
columns of a table.
(For more information, review Section 5.2)
Statistical experiment
A statistical experiment or statistical observation can be thought of as any random activity that
results in a definite outcome.
(For more information, review Section 5.1)
Tree diagram
A tree diagram gives a visual display of the total number of outcomes of an experiment
consisting of a series of events. From a tree diagram, we can determine not only the total
number of outcomes, but also the individual outcomes.
(For more information, review Section 5.3)