Identifying if an experiment is a binomial experiment

[ciline]

There is an example :
A box contains 20 cell phones, and two of them are
defective. Three cell phones are randomly selected from this
box and inspected to determine whether each of them is good
or defective. Is this experiment a binomial experiment?
AND the answer is : NOT a binomial experiment.

if I know that:
A binomial experiment must satisfy the following four
conditions:
1. There are n identical trials.
2. Each trail has only two possible outcomes.
3. The probabilities of the two outcomes remain constant.
4. The trials are independent.

My question is :
1- what do the last two points ( conditions ) mean ?
2- why we consider the example above not to be a binomial experiment ?

 

[jvicens]

1. The third condition means that the probability of success and failure remain the same for each trial. In other words, the probability of getting a good phone and a defective phone should be the same for each of the three trials. The fourth condition means that the outcome of one trial does not affect the outcome of the other trials. In this case, the selection of one phone should not influence the selection of the other phones.

2. The example given is not a binomial experiment because the probabilities of getting a good or defective phone are not constant for each trial. In the first trial, there is a 18/20 (90%) chance of getting a good phone and a 2/20 (10%) chance of getting a defective phone. However, in the second trial, the probabilities change because there are now only 19 phones left in the box, with 17 good phones and 2 defective phones. Similarly, in the third trial, the probabilities change again because there are now only 18 phones left in the box. Therefore, the probabilities of the two outcomes are not constant for each trial, making it not a binomial experiment. Additionally, the trials are not independent since the outcome of one trial affects the probabilities of the other trials.