Glossary
Conditional Probability
The probability of an event occurring given that another event has already occurred. It is denoted as P(B | A), meaning the probability of event B happening given that event A has already happened.
Example:
The Conditional Probability of a student getting an A on a test, given that they studied for more than 5 hours, might be much higher than the overall probability of getting an A.
General Multiplication Rule
A rule used to find the probability that two events, A and B, both occur. It states P(A and B) = P(A) * P(B | A), where P(B | A) is the conditional probability of B given A.
Example:
Using the General Multiplication Rule, you could calculate the probability of drawing a face card and then a 7 from a deck of cards without replacement.
Intersection (∩)
The event where two or more events occur simultaneously. In a Venn diagram, it's represented by the overlapping region of the circles.
Example:
The Intersection of students who take both AP Calculus and AP Statistics would be the group of students enrolled in both courses.
Probability Histograms
Bar graphs that visually represent the probability distribution of different outcomes for a discrete random variable. The x-axis shows the outcomes, and the y-axis shows their corresponding probabilities.
Example:
A Probability Histogram for rolling a fair six-sided die would show six bars of equal height, each representing a probability of 1/6 for outcomes 1 through 6.
Tree Diagrams
Diagrams used to visualize the sequence of outcomes in multi-stage probability processes. Each branch represents a possible outcome, and probabilities are often written along the branches.
Example:
To find the probability of picking two red marbles in a row from a bag without replacement, you could use a Tree Diagram to show the probabilities at each pick.
Two-Way Tables
Tables that organize categorical data into rows and columns, displaying the frequencies or relative frequencies of two variables simultaneously. They are excellent for calculating joint and conditional probabilities.
Example:
A Two-Way Table might summarize data on whether students prefer online or in-person classes, broken down by grade level, making it easy to see preferences within each group.
Union (∪)
The event where at least one of two or more events occurs. In a Venn diagram, it's represented by the entire area covered by the circles involved.
Example:
The Union of students who play soccer or basketball includes anyone who plays soccer, anyone who plays basketball, and anyone who plays both.
Venn Diagrams
Diagrams that use overlapping circles to show the relationships between different sets of outcomes or events. They are particularly useful for visualizing intersections (AND) and unions (OR).
Example:
A Venn Diagram could illustrate the overlap between students who play soccer and students who play basketball, showing the number of students who play both.