multinomial

No. If you keep track of all the numbers that are rolled then there are six possible outcomes, a binomial has only two. It is a multinomial distribution.

buanf

The distribution depends on what the variable is.

If the key outcome is the number on the top of the die, the distribution in multinomial (6-valued), not binomial.

If the key outcome is the number of primes, composite or neither, the distribution is trinomial.

If the key outcome is the number of sixes, the distribution is binomial with unequal probabilities of success and failure.

If the key outcome is odd or even the distribution is binomial with equal probabilities for the two outcomes.

Thus, depending on the outcome of interest the distribution may or may not be binomial and, even when it is binomial, it can have different parameters and therefore different shapes.

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