Supplementary Exercise 5.47 of IPS7e
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(a) a binomial distribution - X ~ Bin(500,1/12), X is the number of
calls reaching a person.

The procedure for making the calls should be considered as simple random
sampling from a finite but very large population. The sampling from a
finite population is not exactly a binomial setting, but when the sample
size is much smaller than the population size (at most 1/20) it is
acceptable to use a binomial distribution. As the sample size here is
truly negligible compared to the population size, it should be fine to use
a binomial distribution.


(b) not a binomial distribution.

The number of trials is not fixed; instead the outcome is the number of
trials needed to succeed. 

As an aside (outside the course curriculum), such situations are often
modelled by so-called negative binomial distributions.
 

(c) not a binomial distribution.

There is no binary (dichotomous, yes/no) outcome.

As an aside (outside the course curriculum), counts such as those described
are often modelled by either Poisson or negative binomial distributions.