Probability

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:
 

• Classical probability
• Empirical probability

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.
 

There are various properties of probability. Some of the most important properties are given below:


Non-Negativity:

This property states that the probability of an event is always greater than or equal to zero. The mathematical representation is:
P(A) ≥ 0

Normalization: 

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

Additivity: 

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)

Complementary Rule: 

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:
 

• Weather Forecasting:
  
  We use probability in weather forecasting to predict what kind of weather would be there for the next day.
  
   
• Business and Finance:
  
  In business and finance, probability is used to assess the risk and returns of various types of investments. It is also used to analyze and predict consumer behavior.
  
   
• Medicine and Healthcare:
  
  In the field of healthcare, probability is used to predict the type of diseases based on the symptoms exhibited by patients.