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In order for a distribution to be considered binomial, one of the key requirements is having a fixed number of trials. This means you have a set number of attempts or tests, known as 'n'. For example, in the original exercise, 1000 different adult respondents were sampled. Here, 'n' is 1000. Each of these 1000 trials represents an individual person being asked a question. Once you decide on the number of trials at the beginning, this number does not change.
Whether you are tossing a coin 100 times or sampling 1000 people, the total 'number' should remain constant throughout the procedure.

Another fundamental component of a binomial distribution is having exactly two possible outcomes for each trial. These outcomes are often referred to as 'success' and 'failure'. In the context of our exercise, the two possible outcomes when respondents are asked if they investigate dates on social media are either 'yes' (success) or 'no' (failure). This binary nature simplifies the modeling of probabilities, making it easy to calculate how often each outcome might occur.
The presence of only two outcomes helps us in applying the binomial distribution without confusion regarding the nature of the results.

The probability of success, denoted as 'p', must remain constant throughout all the trials when dealing with a binomial distribution. This means that each time you perform a trial, the chance of success should be the same. In the exercise, if each respondent had an equal and unchanging probability of answering 'yes', the probability of success would be consistent.
For example, if you flip a fair coin, the probability of getting heads (success) is always 0.5, no matter how many times you flip it. In real surveys, ensuring a constant probability can be difficult, but it is crucial for the binomial model.

Finally, for a distribution to be binomial, each trial must be independent of the others. This means the outcome of one trial should not influence or change the outcome of another trial. In the original exercise, respondents are chosen without replacement. This means once a respondent is selected, they are not put back into the pool of potential respondents.
This lack of replacement violates the independence condition because the outcome of one trial affects the probabilities of the subsequent trials. When trials are not independent, the binomial model becomes less accurate, and you may need to consider other approaches, like the hypergeometric distribution, as mentioned in the solution.