# 4.5 Conditional Probability

Kanya Shah

## Representations of Probability

Being able to calculate and interpret probabilities is important. Be sure to understand how to interpret venn diagrams, two way tables, and tree diagrams.  A two way table or venn diagram can be used to display the sample space and to help find probabilities for a chance process involving two events. A tree diagram shows the sample space of a chance process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities. An example of a Tree Diagram

Image Courtesy of Pinterest An example of a Two-Way Table

Courtesy of MathBits

A venn diagram consists of one or more circles surrounded by a rectangle. Each circle inside the rectangle represents the sample space of the chance process. An example of a Venn Diagram

Courtesy of Pinterest

Conditional probability is the probability that one event happens given that another event is known to have happened. The conditional probability that event B happens given event A has happened is denoted by P(B A).The formula for conditional probability is P(A | B) = P(A and B) P(B)= P(AB)P(B)=P(both events occur)P(given event occurs).
General Multiplication Rule states that the probability that events A and B both occur can be found using this formula for any chance process: P(A | B) = P(AB)=P(A) * P(B | A).

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