10.1 Introduction

We are all used to hearing about probabilities, from the weather forecast to predictions about the stock market to the likelihood of a new business venture succeeding. We often hear things like “a 10% probability of rain” or a “50% chance of success.” We can define probability as the likelihood that some event or condition will occur. Probability is expressed either as a value between 0 and 1 or as a percentage. For example, a probability of 0.35 can also be expressed as 35%.

Probabilities can be continuous or discrete. Continuous probabilities mean that any value within a given range can occur. Discrete probabilities allow only specific values to occur. For example, if only integers are allowed, then the probability is discrete. If any real number is allowed, then the probability is continuous.

Cumulative probability refers to the probability that a random variable is less than or equal to a specific value. If we measure individual probabilities as a number between 0 and 1, then the cumulative probability of a variable is the total area under the probability curve from 0 probability to that value of probability.

A probability distribution is a statistical function that describes all the possible values and likelihoods that a variable can take within the allowable range. This range will be bounded between the minimum and maximum possible values, but precisely where the possible value is likely to be plotted on the probability distribution depends on a number of factors. Probability distributions can be plotted as a curve and can have many different shapes. The specific shape of a probability distribution depends on its characteristics, such as the average value, the range of values, the standard deviation, and so forth. In addition, various types of real-world events can often be characterized as a certain type of probability distribution.

In this lesson, you will first learn about the characteristics of data itself and how those characteristics facilitate calculating or measuring a probability of an event occurring. You will also learn about the various characteristics of probabilities and how they affect the shape of the probability distribution. Finally, we discuss several of the most common types of probability distributions. This entire lesson then provides the foundation to predict outcomes using statistical analysis, which will be explained in the next chapter.