Final answer:
A discrete probability function assigns probabilities to countable outcomes of a discrete random variable. Two rules must be met: probabilities range from zero to one, and the sum of all probabilities must be one.
Step-by-step explanation:
A discrete probability function defines the probability of each possible value of a discrete random variable, which can only take on countable values. These functions differ from those for continuous random variables, which can take on a continuum of values within a given range and are represented by probability density functions where probability is equated to the area under the curve. Two fundamental rules apply to any discrete probability function: Each probability is between zero and one, inclusive. This means that the minimum probability is 0 (impossible event) and the maximum is 1 (certain event). The sum of all probabilities in the distribution must equal one. This ensures that the total probability of all possible outcomes in the sample space adds up to certainty. Common types of discrete probability distributions include binomial and Poisson distributions, among others. However, not all types are covered in elementary courses. It is vital for students to recognize and calculate probabilities with these distributions, familiarizing themselves with concepts such as expected values.