Basic Concepts of Probability

Basic Concepts

• Experiment: An action or situation that can produce a set of outcomes.
• Sample Space: The set of all possible outcomes of an experiment.
• Event: A subset of outcomes of an experiment.
• Probability: A measure of the likelihood of an event occurring.

Probability Rules

• Probability of an Event: A number between 0 and 1 that represents the likelihood of an event occurring.
• Probability of the Sample Space: 1 ( certainty)
• Probability of the Empty Set: 0 (impossibility)
• Complementary Probability: P(A') = 1 - P(A)
• Addition Rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
• Multiplication Rule: P(A ∩ B) = P(A) × P(B)

Types of Probability

• Theoretical Probability: Based on the number of favorable outcomes and the total number of possible outcomes.
• Experimental Probability: Based on the results of repeated trials.
• Conditional Probability: The probability of an event occurring given that another event has occurred.

Independent and Dependent Events

• Independent Events: The occurrence of one event does not affect the probability of another event.
• Dependent Events: The occurrence of one event affects the probability of another event.

Random Variables

• Discrete Random Variable: A random variable that can take on only specific, distinct values.
• Continuous Random Variable: A random variable that can take on any value within a certain range or interval.

Probability Distributions

• Discrete Probability Distribution: A table or formula that describes the probability of each possible value of a discrete random variable.
• Continuous Probability Distribution: A function that describes the probability of a continuous random variable taking on a certain value or range of values.

Basic Concepts

• An experiment is an action or situation that can produce a set of outcomes.
• A sample space is the set of all possible outcomes of an experiment.
• An event is a subset of outcomes of an experiment.
• Probability is a measure of the likelihood of an event occurring.

Probability Rules

• Probability of an event is a number between 0 and 1 that represents the likelihood of an event occurring.
• The probability of the sample space is 1, representing certainty.
• The probability of the empty set is 0, representing impossibility.
• The complementary probability of an event A is 1 - P(A).
• The addition rule for probability is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• The multiplication rule for probability is P(A ∩ B) = P(A) × P(B).

Types of Probability

• Theoretical probability is based on the number of favorable outcomes and the total number of possible outcomes.
• Experimental probability is based on the results of repeated trials.
• Conditional probability is the probability of an event occurring given that another event has occurred.

Independent and Dependent Events

• Independent events are events where the occurrence of one event does not affect the probability of another event.
• Dependent events are events where the occurrence of one event affects the probability of another event.

Random Variables

• A discrete random variable is a random variable that can take on only specific, distinct values.
• A continuous random variable is a random variable that can take on any value within a certain range or interval.

Probability Distributions

• A discrete probability distribution is a table or formula that describes the probability of each possible value of a discrete random variable.
• A continuous probability distribution is a function that describes the probability of a continuous random variable taking on a certain value or range of values.