Explain and apply the concepts of random variables
Definitions: Variable: In statistics, a variable is a characteristic, number, or quantity that can be measured or counted. Random variable: A random variable (RV) is a variable that can take on different values, each with a certain probability. It essentially…
State Bayes Theorem and use it to calculate conditional probabilities
Bayes Theorem Before we move on to Bayes Theorem, we need to learn about the law of total probability. The Law of Total Probability The law of total probability states that if E is an event, and \(A_1, A_2, \cdots A_n\)…
Calculate probabilities using combinatorics, such as combinations and permutations
The Multiplication Principle of Counting Assume that you are conducting an experiment where the outcomes consist of combining two separate actions or tasks. As such, assume that there are \(n\) possibilities for the first task and that for each of…
Define and calculate conditional probabilities
Conditional Probability Given two events \(A\) and \(B\), the conditional probability of event \(A\) occurring, given that event \(B\) has occurred, is the probability of event \(A\) and \(B\) occurring over the probability of event \(B\) occurring as shown by…
Define independence and calculate probability of independent events
Define independence and calculate probabilities of independent events 1.1 Defining Independence In probability and statistics, two events, \(A\) and \(B\), are said to be independent if the occurrence of event A does not affect the probability that the other event…
Calculate Probabilities Using Addition and Multiplication Rules
The Addition Rule The Addition Rule of Probability is a rule for determining is used to find the probability that event A or event B happens. It’s associated with the use of the conjunction “or.” For example, We may want…
Calculate probabilities of mutually exclusive events
Mutually Exclusive Events \(A\) and \(B\) are mutually exclusive events if \(A\) and \(B\) cannot both occur at the same time. For example, when a coin is flipped, it cannot land on both the head and tail simultaneously. Therefore, we…
Define set functions, Venn diagrams, sample space, and events & define probability as a set function on a collection of events and state the basic axioms of probability.
What Is Probability? In mathematics, probability is the branch that deals with numerical descriptions of the likelihood that events will occur or that propositions are true. Probability is a number between 0 and 1, with 0 representing impossibility and 1…
