Last updated on June 18th, 2025
The study of uncertainty, probability is used to measure the likelihood of the occurrence of an event. It is expressed using numbers from 0 to 1. If the probability is 0, then the event will not happen; if the probability is 1, the event will happen. Probability has applications in fields like statistics, science, and engineering.
In mathematics, probability is used to measure the likeliness of the occurrence of an event. The event is represented between the numbers 0 and 1. If the probability is 0, it means the event will not occur. Probability of 1 means the event will definitely happen.
The concept of probability flourished during the 17th century. Mathematicians Blaise Pascal and Pierre de Fermat developed the foundation of probability theory while solving problems for gambling. Over time, probability has evolved and played a crucial role in fields like science, economics and artificial intelligence.
Probability can be divided into two main types based on the experiments, logic, or past data:
Let us look at them one by one
Classical probability is based on the assumption that all outcomes are equally likely in a sample space. For e.g., the probability of rolling a 3 in a fair six-sided die is 1/6
The empirical probability, or most commonly known as experimental probability, is determined by experiments and observations. The probability is calculated as the ratio of favorable outcomes to the total number of trials conducted.
For example, if a coin is tossed 100 times and lands on heads 55 times, the empirical probability of getting heads is 0.55.
This property states that the probability of an event is always greater than or equal to zero. The mathematical representation is:
P(A) ≥ 0
The property of normalization states that the probability of the entire event or sample space is always equal to 1. The mathematical representation is:
P(S) = 1
The property states that, if 2 events A and B are mutually exclusive, then the events cannot occur at the same time. The probability of either event occurring is equal to the sum of their individual probabilities. The mathematical representation is:
P(A ∪ B) = P(A) + P(B)
This property states that the probability of an event not occurring is 1 minus the probability of it occurring. The mathematical representation is:
P(Ac) = 1 - P(A)
Probability is an important concept for students as it helps them develop their critical thinking skills, decision-making skills and analytical skills. Probability helps students get proper understanding of uncertainty, assess risks and make informed decisions for weather predictions, games and financial planning.
We use probability in most of our subjects in academics like statistics, data analysis and research. Learning probability will enhance the student’s problem-solving skills, which prepares them for fields like engineering, medicine and artificial intelligence.
There are a lot of confusions while solving for probability. Students sometimes get confused when solving problems. To curb these confusions, let us see what kinds of tips and tricks the students can use. The tips and tricks are mentioned below:
Understanding the Basics:
Students must first be able to understand the fundamentals of probability like sample space, events and their rules. They must be able to remember the masters, like the formula for classical probability which is
P(A) = Favorable outcomes/Total outcomes
Addition rule: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Use Tree Diagrams and Venn Diagrams:
The use of tree diagrams and Venn diagrams helps the students to understand sequential probabilities and set-based probability questions.
Keep Practicing:
Students must practice solving problems involving probability to understand the concept of probability even better. Practice will make them get some confidence in solving problems quickly and efficiently. This helps the students to get accurate and correct answers.
Probability can be applied in various real-life scenarios and fields. Let us now see the fields where probability is applied:
Learning and working with probability can be tricky as even small mistakes can lead to errors. Understanding the common mistakes will help us improve accuracy and make better predictions.
What is the probability of getting heads when tossing a fair coin?
The probability of getting heads when tossing a coin is 50%
A fair coin has two equally likely outcomes: heads (H) and tails (T).
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes:
P(H) = favorable outcomes/Total Outcomes = 1/2 = 0.5 or 50%
What is the probability of rolling a 3 on a fair six-sided die?
The probability of rolling a 3 is ⅙.
There are six equally likely outcomes in a fair die with 6 faces: 1, 2, 3, 4, 5, and 6.
Hence, the probability of getting a number is the number of favorable outcomes divided by the total number of outcomes.
Hence, P(3) = 1/6
What is the probability of drawing a heart from a standard deck of 52 cards?
The probability of drawing a heart from a deck of 52 cards is 25%.
A standard deck of cards has 52 cards, out of which 13 are hearts.
We use a formula, where the number of favorable outcomes is divided by the number of outcomes.
Hence, P(H) = 13/52 = 0.25 or 25%
What is the probability of getting heads when tossing two fair coins?
The probability of getting two heads when tossing two coins is 0.25 or 25%
The possible outcomes when two coins are tossed are HH, HT, TH, and TT.
Only one outcome has two heads when the coins are tossed.
Hence, P(HH) = 1/4 = 0.25 or 25%
What is the probability of rolling a sum of 7 when rolling two fair six-sided dice?
1/6
The combinations that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).
There are 6 favorable outcomes out of a total of 36 possible outcomes.
We can use the formula to find the probability.
Hence, P(sum of 7) = 6/36 = 1/6.
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!