Basic Concepts of Probability

random experiment: is a mechanism that produces a definite outcome that cannot be predicted with certainty

sample space: associated with a random experiment is the set of all possible outcomes

event: is a subset of the sample space

An event E is said to occur on a particular trial of the experiment if the outcome observed is an element of the set E.

The probability of an outcome e in a sample space S is a number p between 0 and 1 that measures the likelihood that e will occur on a single trial of the corresponding random experiment. The value p = 0 corresponds to the outcome e being impossible and the value p = 1 corresponds to the outcome e being certain.

The probability of an event A is the sum of the probabilities of the individual outcomes of which it is composed. It is denoted P(A).

Takeaways

• The sample space of a random experiment is the collection of all possible outcomes.
• An event associated with a random experiment is a subset of the sample space.
• The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.
• The probability of any event A is the sum of the probabilities of the outcomes in A.