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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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What is the probability of rolling a number greater than or equal to 3?
The answer depends on what you are rolling: a number cube or some other shape? For a die, the answer is 2/3.
Define a normal random variable?
I have included two links. A normal random variable is a random variable whose associated probability distribution is the normal probability distribution. By definition, a random variable has to have an associated distribution. The normal distribution (probability density function) is defined by a mathematical formula with a mean and standard deviation as parameters. The normal distribution is ofter called a bell-shaped curve, because of its symmetrical shape. It is not the only symmetrical distribution. The two links should provide more information beyond this simple definition.
How many rolls to have a 50 percent probability to get each number at least once d6?
Depends on what you are rolling - a cubic die or a more exotic shape.
What is the probability of rolling a number cube a number less than 5 and spin a number greater than 5?
There is insufficient information on the shape of the spinner.
What is the probability of rolling a number less than 3 and then rollong a prime number?
The question depends on what the numbers are being rolled on: a hexahedron or some other shape.
