Probability Issues? Help Solving Joe's Die Problem

[dann]

Having terrible time learning probabilities - so this question threw me.
Joe throws a die 4 times, what is probability of him getting a number 1 at most once? Hope you can help - learning binomial formulas, poisson & hypergeometric. Hope someone can assist.

 

[Ackbach]

Well, this situation satisfies the four criteria for a binomial distribution:

Binary: the trial has to have a "success" (getting a 1) or "failure" (not getting a 1).
Independent: the trials have to be independent, one from another.
Number: the number of trials has to be fixed.
Success: the probability of success has to be the same from trial to trial.

So, what is the parameter $p$, and how many trials $n$ are there?