The binomial distribution applies to the number of times an event occurs
out of n trials, when each trial is independent and the probability is
the same on each trial. The classic example is coin flips, e.g. number
of heads in n trials. In that case p = 0.5, the probability of a head on
But you could easily cook up other examples with cards or dice. The
number of times X happens with cards (like you get a red jack, or a
number less than 10, or a pair of 3s from a deal of 5 cards), if after
each trial you put all the cards back and shuffle the deck. The number
of times X happens with a roll of one die, or two, or 3.
Or anything else where you arrange that the probabilities are the same
each time. The number of times you draw a blue marble from a collection,
if you put the marble back each time. The number of times you get a red
sock out of your drawer with your eyes closed, if you put it back each
The key is that you reset things each time, so p is always the same for the next trial.