A binomial experiment , called also binomial trials,
consists of the sequence of simpler identical experiments that have two possible
outcomes each. The independent events 
represent
successes in consecutive
experiments. We assume that we have an infinite sequence
of events 
that are independent and have the same
probability 
. We denote by 
the failure in the j-th
experiment, and put q=1-p.
Two important random variables are associated with the binomial experiment are the number X of successes in n trials, and the number T of trials until first success.
Random variables are often described solely in terms of cumulative distribution
function F(x), or formulas for 
without reference to the underlying
probability space 
. For instance, the number of minutes T that
we spend waiting for a bird to come to the bird feeder at the back of my house is random,
and I believe 
because 
.
It is intuitively obvious that on average we get np successes in n trials.
It is perhaps less obvious
that on average we need 1/p trials to get the first success.
| 2n |  | Frequency in 1000 trials |  |
| 100 | 0.07959 | 0.08200 | 0.56278 |
| 300 | 0.04603 | 0.06100 | 0.56372 |
| 500 | 0.03566 | 0.03700 | 0.56391 |
| 700 | 0.03015 | 0.02200 | 0.56399 |
