An experiment has four equally likely outcomes: E1, E2, E3,...

An experiment has four equally likely outcomes: $E_{1}, E_{2}, E_{3},$ and $E_{4}$ a. What is the probability that $E_{2}$ occurs? b. What is the probability that any two of the outcomes occur (e.g., $E_{1}$ or $E_{3}$ )? c. What is the probability that any three of the outcomes occur (e.g., $E_{1}$ or $E_{2}$ or $E_{4}$ )?

An experiment has four equally likely outcomes: $E_{1}, E_{2}, E_{3},$ and $E_{4}$
a. What is the probability that $E_{2}$ occurs?
b. What is the probability that any two of the outcomes occur (e.g., $E_{1}$ or $E_{3}$ )?
c. What is the probability that any three of the outcomes occur (e.g., $E_{1}$ or $E_{2}$ or $E_{4}$ )?

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Key Concepts

Equally Likely Outcomes

This concept means that each outcome in the sample space has the same probability of occurring. When outcomes are equally likely, the probability of any particular outcome is the reciprocal of the total number of outcomes.

Sample Space

The sample space is the complete set of all possible outcomes of an experiment. It provides the foundation for determining probabilities, as each event's likelihood is measured relative to the total number of outcomes in the sample space.

Counting Techniques

Counting techniques help determine the number of favorable outcomes when dealing with events involving multiple outcomes. This involves using basic combinatorial methods such as combinations and the addition principle, which are essential for computing probabilities of compound events.

Probability of Combined Events

When an event consists of several outcomes (for instance, the occurrence of any two or three outcomes), its probability is the sum of the probabilities of each mutually exclusive outcome. This approach utilizes the basic probability definition in combination with counting techniques to account for all favorable outcomes.

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