The sum of the probabilities in a probability distribution is always 1. A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment. Based on this definition, a probability distribution has two important properties that are always true: Each probability in the distribution must be of a value between 0 and 1. The sum of all the probabilities in the distribution must be equal to 1. An example: You could define a probability distribution for the observation for the number displayed by a single roll of a die. The probability that the die with show a "1" is 1 6 . That's because there are six possible outcomes, and only one of those outcomes is a "1". Lets label the probabilities of all the possible outcomes for the single die. Roll a "1": Probability is 1 6
Roll a "2": Probability is 1 6
Roll a "3": Probability is 1 6
Roll a "4": Probability is 1 6
Roll a "5": Probability is 1 6
Roll a "6": Probability is 1 6 Each probability is between 0 and 1, so the first property of a probability distribution holds true. And the sum of all the probabilities: 1 6 + 1 6 + 1 6 + 1 6 + 1 6 + 1 6 = 1 , so the second property of a probability distribution holds true.
