List of Possible Outcomes and Probabilities

E

The probability distribution shows the outcomes with corresponding probabilities.

The correct answer is E. Probability distribution.

A probability distribution is a listing or representation of all possible outcomes of an experiment along with their corresponding probabilities of occurrence. It provides a systematic way to describe the likelihood of each outcome.

In probability theory, an experiment refers to a process or event that can result in multiple outcomes. These outcomes may have different probabilities associated with them. The probability distribution captures this information and presents it in a structured format.

The probability distribution can take different forms depending on the nature of the experiment. For discrete random variables, which have a finite or countable number of possible outcomes, the probability distribution is often presented as a table, listing each possible outcome along with its probability. The probabilities assigned to each outcome must satisfy certain properties, such as summing to 1.

For example, let's consider a fair six-sided die roll. The possible outcomes are the numbers 1, 2, 3, 4, 5, and 6. Since the die is fair, each outcome has an equal probability of 1/6. The probability distribution for this experiment would be:

Outcome Probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6

On the other hand, for continuous random variables, which can take on any value within a range, the probability distribution is often described using a probability density function (PDF) or cumulative distribution function (CDF).

In summary, a probability distribution is a comprehensive listing or representation of all possible outcomes of an experiment, along with their corresponding probabilities. It helps in understanding the likelihood of different outcomes and plays a fundamental role in probability and statistics.