PS - Probability and Statistics Module Overview

Probability and Statistics Introduction

How do we know smoking causes lung cancer? How do we know medical tests really work? These questions can be answered with experimental probabilities. In this unit, we will discuss theoretical and experimental probabilities and what they can tell us about the world around us. Using Venn diagrams, two way tables, and tree diagrams, you will analyze data and use it to answer questions. From the simple, "How much food should my restaurant buy?", to the more serious, "What does this positive medical test result really mean?"

Essential Questions

• How can I use a Venn diagram to organize various sets of data?
• How are intersections and unions of sets like other intersections and unions?
• How can two-way frequency tables be useful?
• How are everyday decisions affected by an understanding of probability?
• What does it mean for two events to be independent?

Key Terms

The following key terms will help you understand the content in this module.

Addition Rule - The probability for the union of two sets is equal to the sum of the probabilities of the two sets minus their intersection: P(AUB)=P(A)+P(B)-P(A∩B).

Complement - Given a set A, the complement of A, denoted A' , is the set of elements that are not members of A.

Conditional Probability - The probability of an event A, given that another event, B, has already occurred; denoted P(A|B). The formula for a conditional probability is P(A given B) = [P(A and B)] / P(B).

Dependent Events - Two or more events in which the outcome of one event affects the outcome of the other event or events.

Element - A member or item in a set.

Independent Events - Events whose outcomes do not influence each other.

Intersection of Sets - The set of all elements contained in all of the given sets, denoted by .

Multiplication Rule for Independent Events - The formula is P(A∩B)=P(A)*P(B).

Mutually Exclusive Events - Two events that cannot occur simultaneously, meaning that the probability of the intersection of the two events is zero; also known as disjointed events.

Outcome - A possible result of an experiment.

Overlapping Events - Events that can occur simultaneously - they have an intersection.

Sample Space - The set of all possible outcomes from an experiment.

Set - A collection of numbers, geometric figures, letters, or other objects that have one or more common characteristics.

Subset - A set in which every element is also contained in a larger set.

Tree Diagram - Branching probability diagram showing a series of events.

Union of Sets - The set of all elements that belong to at least one of the given two or more sets denoted ∪.

Venn Diagram - A picture that illustrates the relationship between two or more sets.

 IMAGES CREATED BY GAVS