Question

What are the four conditions that need to be satisfied for a binomial setting?

Answer 1

In a BInomial setting there are two possible outcomes per event.

The important conditions for using a binomial setting in the first place are:

• There are only two possibilities, which we will call Good or Fail
• The probability of the ratio between Good and Fail doesn't change during the tries
• In other words: the outcome of one try does not
  influence the next

Example :
You roll dice (one at a time) and you want to know what the chances are that you roll at lest 1 six in 3 tries.
This is a typical example of binomial:

• There are only two possibilities:
  6 (chance `=1/6`) or not-6 (chance `=5/6`)
• The die has no memory, so:
• Every next roll has still the same probabilities.

You can set up a chance-tree, but you can also calculate the chance of three Fails, which is

`5/6*5/6*5/6=125/216`

And your chance of succeeding would be

`1-125/216=91/216`