Understanding Probability
Learn the fundamental concepts of probability theory.
Probability is a measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
Basic Probability Formula:
P(Event) = Number of favorable outcomes / Total number of possible outcomes
This formula applies when all outcomes are equally likely.
Key Probability Concepts:
Sample Space
The set of all possible outcomes of an experiment.
Example: When rolling a die, the sample space is 6.
Event
A subset of the sample space.
Example: Rolling an even number is the event 6.
Probability of an Event
The measure of the likelihood of the event occurring.
Example: P(rolling an even number) = 3/6 = 1/2.
Complementary Events
Events A and A' are complementary if P(A) + P(A') = 1.
Example: P(not rolling a 6) = 1 - P(rolling a 6) = 1 - 1/6 = 5/6.