Probability in Maths Last Updated : 16 May, 2025 Comments Improve Suggest changes Like Article Like Report Probability is the branch of mathematics where we determine how likely an event is to occur. It is represented as a numeric value ranging from 0 to 1. Probability can be calculated as:\text{Probability} = \dfrac{Favourable \ Outcome}{Total \ Number \ of \ Outcomes}Favourable outcomes refer to the outcome we are interested in.Total outcomes represent the complete set of possible results an event can produce.Below are a few examples illustrating the concept of probability in different situations:Examples of ProbabilityWhat are the chances of the following events when we pick a random number from 1 to 10 ?The number is divisible by 1100% are divisible by 1, as all numbers are completely divisible by 1, so we say probability is 1.The number is divisible by 110% are divisible by 11 as, none of the number is divisible by 11 as they are greater, so we say probability is 0.The number is divisible by 250% are divisible by 2, numbers like (2, 4, 6, 8, 10), so we say probability is 1/2.The number is divisible by 520% are divisible by 5, numbers like (5 and 10) so we say probability is 1/5.Probability for BeginnersIn this section, you will explore the fundamental concepts of probability, key formulas, conditional probability, and Bayes' Theorem. By the end, you'll have a clear understanding of how probability is applied in real-life situations and develop the skills needed to solve related problems.Basic Concepts of ProbabilityProbability FormulasEvents in ProbabilityConditional ProbabilityBayes' TheoremReal-Life Applications of ProbabilityProbability for Aptitude PreparationProbability-based questions are commonly asked in various examinations, such as placement tests and government-related exams. In this section, we will explore these types of questions, along with tricks and shortcuts to solve them quickly. Additionally, we will cover some interesting facts about probability to enhance your aptitude preparation.Probability Tricks Interesting Facts on ProbabilityProbability – Aptitude QuestionsProbability Practice QuestionsPractice the knowledge you've acquired about probability through these practice questions (organized by difficulty level), along with other topics in probability, and take a quiz for a mock test.Easy Level Probability Questions Medium-Level Probability QuestionsHard-Level Probability QuestionsBinomial Distribution PracticeConditional Probability Practice Probability Quiz Probability for ProgrammersFor coders who wish to implement probability concepts in a specific programming language, this section covers key topics such as reaching points in steps, maximum sums, arithmetic progressions, and the Birthday Paradox.Probability of reaching a point in 2 or 3 stepsProbability of the maximum weighted pairProbability of maximum sum in an arrayProbability of numbers in APBirthday ParadoxProbability of reaching all points in N movesAdvanced Topics on ProbabilityThis section covers advanced probability topics, including random variables, Poisson and binomial distributions, and probability distribution functions.Probability Theory Random VariablePoisson DistributionProbability DistributionProbability Distribution FunctionBinomial DistributionGeometric DistributionMarginal Distribution Comment More infoAdvertise with us Next Article Events in Probability A abhishek1 Follow Improve Article Tags : Mathematics School Learning Probability Tutorials Maths-Categories Math Tutorials +2 More Similar Reads Probability in Maths Probability is the branch of mathematics where we determine how likely an event is to occur. It is represented as a numeric value ranging from 0 to 1. Probability can be calculated as:\text{Probability} = \dfrac{Favourable \ Outcome}{Total \ Number \ of \ Outcomes}Favourable outcomes refer to the ou 4 min read Events in Probability Events in Probability- In Probability, an event can be defined as any outcome or set of outcomes from a random experiment. In other words, an event in probability is the subset of the respective sample space.Example:1. If you roll a die, the event could be "getting a 3" or "getting an even number."2 14 min read Types of EventTypes of Events in ProbabilityWhenever an experiment is performed whose outcomes cannot be predicted with certainty, it is called a random experiment. In such cases, we can only measure which of the events is more likely or less likely to happen. This likelihood of events is measured in terms of probability and events refer to t 13 min read Mutually Exclusive EventsMutually exclusive events are those that cannot occur at the same time; if one event happens, it eliminates the possibility of the other event occurring. For example, in a cricket match between India and Pakistan, only one team can win. If Pakistan wins, India loses, and vice versa. Therefore, "Indi 8 min read Probability Based on CoinTossing a Coin Probability FormulaCoin Toss Probability helps us to determine the likelihood of getting heads or tails while flipping a coin. Before diving into the formula, it's essential to understand that when a fair coin is tossed, there are only two possible outcomes: Heads (H) and Tails(T). In the fair coin toss definition, ea 7 min read What are all the possible outcomes if a coin is tossed?When a fair coin is tossed then there are two possible outcomes: H (head)T (tail)The probability of occurrence of both events will be 0.5.What is Probability?Probability is a mathematical branch that deals with calculating the likelihood of occurrence of a random event. Its value ranges between 0 (e 6 min read How many possible outcomes would be there if three coins were tossed once?Total Possible Outcomes = 2^3 = 8 Explanation:We will learn 2 Methods on how to solve this problem :1) Logical MethodStep 1: First of all try to find out all the possible outcomes when a single coin is toss. When we toss a fair coin then the outcomes are 'Head' or 'Tail'Step 2: Represent them in for 7 min read How to calculate Dice Probabilities? Probability is the chance or likelihood of an event happening. It is represented by a number between 0 and 1. The higher the probability, the greater the chances of the event occurring.A probability of 0 means the event is impossible and cannot happen.A probability of 1 means the event is certain to 5 min read CardsWhat is the probability of not picking a king if you choose randomly from a pack of 52 cards?In one pack of cards, there are 4 kings in a deck of 52, therefore , the probability of drawing a king is = Probability of an event, P(A) = Favorable outcomes / Total number of outcomes= 4/52= 1/13Hence, the probability of not picking a king P(B) = 1 - P(A)= 1 - 1/13= 12/13Therefore the probability 7 min read Find the probability that if one card drawn from a well-shuffled pack of 52 playing cards is a face card?Answer: The probability of getting a face card = Favorable outcomes / Total outcomes = 12 / 52 = 3/13Probability means Possibility. It states how likely an event is about to happen. The probability of an event can exist only between 0 and 1 where 0 indicates that the event is not going to happen i.e 7 min read What is the probability of getting either a red card or King card?A probability is a number that expresses the chance or likelihood of an event occurring. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%, where 0 indicates an impossible event and 1 indicates a certain event. The sum of the probabilities 8 min read What is the probability of drawing a black card from a well-shuffled deck of 52 cards?Answer: Therefore probability of getting a black card= {total number of black cards in the deck}/{total number of cards in the deck}= 26/52= 1/2A branch of mathematics that deals with the happening of a random event is termed probability. It is used in Maths to predict how likely events are to happe 5 min read Axiomatic Approach to Probability Hearing the word "probability" brings up ideas related to uncertainty or randomness. Although the concept of probability can be hard to describe formally, it helps us analyze how likely it is that a certain event will happen. This analysis helps us understand and describe many phenomena we see in re 10 min read Addition Rule for Probability Probability is an experimental approach to the game of chances we come across every day in our lives. It is a way to describe these “chances†mathematically and then analyze them. It allows us to measure the chances of something occurring. Probability of Event P(E) = [Number of Favorable Outcomes] / 9 min read Conditional Probability Conditional probability defines the probability of an event occurring based on a given condition or prior knowledge of another event. Conditional probability is the likelihood of an event occurring, given that another event has already occurred. In probability, this is denoted as A given B, expresse 12 min read Bayes' Theorem Bayes' Theorem is a mathematical formula that helps determine the conditional probability of an event based on prior knowledge and new evidence.It adjusts probabilities when new information comes in and helps make better decisions in uncertain situations.Bayes' Theorem helps us update probabilities 12 min read Like