Probability & Sample Space: Polling Context

• Probability is between zero and one.
• Zero indicates impossibility.
• One indicates certainty.
• An experiment is determining one of many possible outcomes.
• A sample space is all the possible outcomes.

Poll Sample Space

• A sample in a nationwide public opinion survey is the total population of people who could potentially be surveyed.
• An event is the subset of people chosen to participate in the poll.
• In a polling sample, a person is either asked to participate or not.
• Participation and nonparticipation comprise all possible outcomes.
• These events are exhaustive, and are mutually exclusive .
• Participation in the poll automatically excludes someone from being a non participant in the poll.

Union

• Multiple events can form a union.
• If two separate events A and B form a union, then the potential outcomes of A union B include all possible outcomes of event A or event B.
• An outcome of event B is considered a possible outcome of A union B, even if the outcome is not possible in event A and vice versa.
• The union of events A and B is represented in a Venn diagram with circles A and B in circles that are entirely shaded to indicate that an outcome of either event A or event B qualifies.

Intersection

• Events A and B can form an intersection.
• The event is made up of all outcomes shared by A and B.
• The intersection of A and B is represented in a Venn diagram by the portion where A and B overlap, which is shaded in.

Event Complement

• The complement of event A is denoted by A with a superscript C.
• it represents all events existing outside of event A.
• Event A is represented by a red circle.

Probability Types

• Subjective, empirical, and classical probability are used to assign probabilities to events.
• Subjective probabilities are based on an individual's opinion or experience without reference to any data.
• Empirical probabilities are the observed frequency of an outcome of an event.
• They need actual observations or experiments that are repeated several times to generate the large amount of data to draw an accurate conclusion.
• Classical probabilities are based on mathematical calculations, logic, and the assumption that all outcomes of an experiment are equally likely.

Card Example

• There is only one queen of hearts in a 52 card deck.
• The probability of drawing this card is one out of 52.

Importance

• Using subjective, empirical or classical probabilities allows practicing prediction in a situation of uncertainty.
• Knowing how to interpret probabilities accurately enables making an informed decision.

Explanation of probability, impossibility, and certainty in polling sample spaces. Demonstrates the creation of a sample space and the ways in which participation and nonparticipation are mutually exclusive. Introduction to the concept of a union between two events, A and B.