Internet sites often vanish or move so that references to them cannot be followed. In fact, 13 % of Internet sites referenced in major scientific journals are lost within two years after publication.
If a paper contains nine Internet references, what is the probability that all nine are still good two years later?
What specific assumption must be made in order to calculate the probability?

a. One does not need to make any assumptions; this is just a straightforward calculation.
b. The occurrence of the site references in the paper are disjoint events.
c. The occurrence of the site references in the paper are independent events.
d. The paper containing the references must be obtained by random sampling.

For each reference, there are only two possible outcomes. Either it is still good two years later, or it has vanished. So we should try to use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

However, the binomial probability distribution can only be used if the events are independent from each other.

So the correct answer is:

c. The occurrence of the site references in the paper are independent events.