Question

In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are returned once employees are done with them. You are the 5^th employee to take a pen. Is this a binomial experiment?

Answer 1

For binomial experiment we need followings:

1. the possible results of any trial can be divided into two classes, which we conveniently call "success" and "failure";

2. the trials are independent

3. the probability of success remains constant from trial to trial.

Here if we define a random variable X as

X=1 if employee takes a pen which does not work

=0 otherwise.

If we define success by taking a pen which does not work then Condition 1 is satisfied. However if the employees are used pen at a time then success probability is not fixed at all. So if for every time there are 12 pens when employee is going to use pen then chance of success=1/12 is fixed for trial to trial and trials are independent and then this is binomial experiment.