Probability: Basic Concepts and Addition/Multiplication Laws Probability is a measure of the likelihood that an event will occur. It is expressed as a number...
Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Basic Concepts:
Sample space: The set of all possible outcomes for a random experiment.
Event: A specific outcome within the sample space.
Probability mass function (PMF): A function that assigns a probability to each element in the sample space. The sum of the PMF of all possible outcomes must equal 1.
Probability distribution: A collection of probabilities associated with different events in the sample space.
Random variable: A function that assigns a probability to each possible outcome.
Addition/Multiplication Laws:
These laws apply to probabilities of events in independent experiments.
Addition: P(A + B) = P(A) + P(B)
Multiplication: P(AB) = P(A) * P(B)
These laws allow us to calculate the probability of multiple events occurring together.
Examples:
Probability of rolling a 6 on a standard six-sided die is 1/6.
Probability of getting a head when flipping a coin is 1/2.
Probability of selecting red from a bag containing 5 red and 3 blue balls is 5/8.
By understanding these basic concepts and the addition/multiplication laws, we can calculate the probability of various events and make informed predictions about the future