A probability experiment is conducted in which the sample...

A probability experiment is conducted in which the sample space of the experiment is, $S=\{1,2,3,4,5,6,7,8,9,10,11,12\} .$ Let event $E=\{2,3,4,5,6,7\},$ event $F=\{5,6,7,8,9\},$ event $G=\{9,10,11,12\},$ and event $H=\{2,3,4\} .$ Assume each outcome is equally likely. List the outcomes in $F$ or $G .$ Now find $P(F \text { or } G)$ by counting the number of outcomes in $F$ or $G .$ Determine $P(F \text { or } G)$ using the General Addition Rule.

A probability experiment is conducted in which the sample space of the experiment is, $S=\{1,2,3,4,5,6,7,8,9,10,11,12\} .$ Let event $E=\{2,3,4,5,6,7\},$ event $F=\{5,6,7,8,9\},$ event $G=\{9,10,11,12\},$ and
event $H=\{2,3,4\} .$ Assume each outcome is equally likely.
List the outcomes in $F$ or $G .$ Now find $P(F \text { or } G)$ by counting the number of outcomes in $F$ or $G .$ Determine $P(F \text { or } G)$ using the General Addition Rule.

Key Concepts

Sample Space

The sample space of a probability experiment is the set of all possible outcomes. It forms the basis of probability calculations, as it provides the total number of outcomes against which any event’s outcomes can be compared.

Equally Likely Outcomes

In experiments with equally likely outcomes, each individual outcome in the sample space has the same probability of occurring. This assumption is fundamental for calculating probabilities by simply counting outcomes.

Event

An event is a subset of the sample space, representing a collection of outcomes that share a common property or satisfy a certain condition. Understanding events as subsets allows us to apply set operations when calculating probabilities.

Union of Events

The union of events refers to the set of outcomes that belong to at least one of the events. It is denoted by the word 'or' in probability questions and is a key concept when combining events to find overall probabilities.

Counting for Classical Probability

When every outcome is equally likely, the probability of an event is calculated as the number of outcomes in the event divided by the total number of outcomes in the sample space. This method of counting is central to classical probability.

General Addition Rule

The General Addition Rule is used to calculate the probability of the union of two events. It states that P(A or B) equals P(A) plus P(B) minus the probability of both events occurring. This rule corrects for any overlap, ensuring that outcomes that belong to both events are not counted twice.

Intersection of Events

The intersection of two events is the set of outcomes that are common to both events. This concept is particularly important in the General Addition Rule, where the probability of the intersection is subtracted to account for overlapping outcomes in the union.

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