In God we trust.
All others must bring data.
Robert Hayden,
Plymouth State
College
Chapter 8
Sec 8.1
Frequently we encounter situations where there are only two outcomes of
interest like:
tossing a coin to yield heads or tails, attempting a free throw in basketball
which will either be successful or not, predicting the sex of an unborn child
(either male or female), quality testing of parts which will either meet
requirements or not. In each case we can describe the two outcomes as
either a success or a failure depending on how the experiment is defined.
When four specific conditions are satisfied in an experiment it is called a
BINOMIAL setting which will produce a BINOMIAL DISTRIBUTION. The four
requirements are:
1) each observation falls into one of two categories called a success or
failure
2) there is a fixed number of observations
3) the observations are all independent
4) the probability of success (p) for each observation is the same 
equally likely
Statistics jargon: If the experiment is a binomial setting, then the
random variable X = number of successes and is called a binomial random
variable, and the probability distribution of X is called a binomial
distribution
BINOMIAL DISTRIBUTION DEFINED::
The distribution of the count X of successes in the binomial setting is the
binomial distribution with parameters n and p. The parameter n is the
number of observations, and p is the probability of a success on any one
observation. The possible values of X are the whole numbers from 0 to n
and is written X is B(n,p).
The binomial distributions are an important class of discrete probability
distributions. See page 440441 for examples. The TI 83 can
calculate binomial probabilities as described in Ex. 8.5 page 442.
pdf (probability
distribution function, specifically binomial pdf)... Given a discrete random variable X, the probability distribution function assigns a probability to each value of X. The probabilities must satisfy the rules for probabilities studied earlier. 
Frequently we want to find the probability that a random variable takes a range
of values...the cuulative binomial probability cdf or specifically binomial cdf.
cdf
(cumulative (probability) distribution function, specifically
binomial cdf)... 
In addition to being helpful in answering questions involving wording such as "find the probability that it takes at most 6 trials," the cdf is also particularly useful for calculating the probability that it takes more than a certain number of trials to see the first success using the complement rule...
P(X > n) = 1  P(X < n) n = 2, 3, 4, ... 
Binomial formulas exist to computer these probabilities by hand.
We must first consider the
Binomial coefficient...

Binomial Probability
The
number of ways of arranging k successes among n observations is
given by the binomial coefficient P(X=k) =
