Question

For which of the following counts would a binomial probability model be reasonable?

All of the answer options are correct.

the number of sevens in a randomly selected set of five digits

from your table of random digits, the number of hearts in a hand of five cards dealt from a standard deck of 52 cards that has been thoroughly shuffled

the number of phone calls received in a one-hour period

Answer 1

The number of sevens in a randomly selected set of five digits

A probability distribution is binomial if it can have only 2 possible outcomes, the probability of success is constant on all trials and the number of trials are fixed.

Only in the case of selecting 5 digits randomly, the probabilty of selecting a 7 is constant and the only two outcomes are '7' or 'not 7'. The number of trials is fixed as 5. Therefore, this is a binomial experiment. When cards are dealt, cards are not dealt with replacement and hence, the probability of success varies on each trial. The number of phone calls received can have more than two of values. Therefore, that is also not a binomial variable.