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1. Overview of Probability
In this lesson, we’ll learn what a probability is, and learn about important probability concepts like events, complements and expected value. We’ll also learn how to calculate basic probabilities.
Lesson Goal (00:34)
The goal of this lesson is to learn what probability is, and calculate some simple probabilities.
Events and Probabilities (00:40)
An event is an outcome or combination of outcomes that can occur from a process. For example, if we roll a dice, possible events include rolling a 4, rolling an even number, and so on. When we roll a dice, any valid event will either occur or not occur.
A probability is a numeric value that measures how likely it is that some event of interest will occur. To calculate the probability of an event, we divide the number of outcomes where the event occurs by the total number of possible outcomes. For example, when we roll a dice, there are 3 possible even numbers out of 6 possible outcomes, so the probability of rolling an even number is 3/6, or ½.
Probability Properties (03:44)
All probabilities have a value between 0 and 1. An event with a probability of zero will definitely not occur. An event with a probability of one will definitely occur. The higher the probability of an event, the more likely it is to occur. We can express probabilities using fractions, decimals, or percentages.
The complement of an event is the set of outcomes where the event does not occur. For example, the complement of rolling a two is rolling any number other than two. An event and its complement cannot occur at the same time, but one must always occur. As a result, the probability of an event and its complement add to one, and we can find the probability of a complement by subtracting the event’s probability from one.
Expected Value (05:51)
The expected value of a variable is the predicted value of that variable, based on the probability and value of each possible outcome. To calculate expected value, we multiply the value of each outcome by its probability, and add the result for each possible outcome.
As we adjust the value of each possible event, or the probability of each possible event, the expected value changes. We can use the expected value to determine if a process, such as a dice game, has any value to us.