Basic Concepts of Probability Probability is a branch of mathematics that deals with the likelihood or certainty of certain events occurring. It is used to...
Basic Concepts of Probability
Probability is a branch of mathematics that deals with the likelihood or certainty of certain events occurring. It is used to quantify the degree of certainty associated with an event and is expressed as a numerical value between 0 and 1.
A probability of 0 means that the event is certain to not occur, while a probability of 1 indicates that the event is certain to occur. The probability of an event is determined by its likelihood and the total number of possible outcomes in the sample space.
For example, suppose you roll a fair six-sided die. The total number of possible outcomes is 6, and each side has an equal probability of being rolled. The probability of rolling a specific number, say 6, is 1/6. This means that the likelihood of rolling 6 is 1/6, regardless of the other rolls.
Key Concepts:
Sample space: The set of all possible outcomes in a random experiment.
Event: A subset of the sample space that represents a particular outcome.
Probability mass function (PMF): A function that assigns a probability to each event in the sample space.
Probability density function (PDF): A function that assigns a probability density to each point in the sample space.
Independent events: Events that occur with the same probability regardless of the occurrence of other events.
Conditional probability: The probability of an event occurring given that another event has already occurred.
Bayes' theorem: A theorem that relates probabilities of events conditional on each other