Decide on the situation for which you want to set up a probability distribution. This can be anything from picking colored balls out of a hat, flipping three coins, rolling dice or spinning a roulette wheel. Make sure that the situation is mathematical and countable.
List every possible outcome on a sheet of paper. Flipping two coins simultaneously, for example, must produce tails/tails, tails/heads, heads/tails or heads/heads. Add up groups of possibilities to make the job go faster, such as writing 18 black, 18 red and 2 green to describe the possibilities when playing roulette. Be as specific or as general as the requirements for the probability distribution dictate. Write neatly and carefully; even a small error can make the probability distribution inaccurate and misleading.
Leave the number of possible outcomes separate and distinct, combine them, or separate them, based on the stated requirements for the probability distribution. Choose an event and divide its value by the sum of all possible events to calculate the probability of that event occurring. For example, the probability of landing in a black roulette pocket, under ideal circumstances, is 18/38, or .4737. Multiply the decimal value by 100 to find the percentage probability. Continue this process with all the other events until every event is given a decimal probability. Sum up all of the decimal probabilities when you are finished. They should add up to exactly 1.00. Start over and calculate more carefully if they do not add up to 1.00.
Draw two columns side by side on a piece of paper. Label the first column with the name of the event you are investigating, such as "number of tails" or "values of a die." Label the second column "probability." Write each event neatly in the space under the first column. Write the decimal probabilities next to each event. Continue until every event has an associated probability. Add up all the probabilities one more time to ensure the sum is 1.00. Title the probability distribution.