agra,ahmedabad,ajmer,akola,aligarh,ambala,amravati,amritsar,aurangabad,ayodhya,bangalore,bareilly,bathinda,bhagalpur,bhilai,bhiwani,bhopal,bhubaneswar,bikaner,bilaspur,bokaro,chandigarh,chennai,coimbatore,cuttack,dehradun,delhi ncr,dhanbad,dibrugarh,durgapur,faridabad,ferozpur,gandhinagar,gaya,ghaziabad,goa,gorakhpur,greater noida,gurugram,guwahati,gwalior,haldwani,haridwar,hisar,hyderabad,indore,jabalpur,jaipur,jalandhar,jammu,jamshedpur,jhansi,jodhpur,jorhat,kaithal,kanpur,karimnagar,karnal,kashipur,khammam,kharagpur,kochi,kolhapur,kolkata,kota,kottayam,kozhikode,kurnool,kurukshetra,latur,lucknow,ludhiana,madurai,mangaluru,mathura,meerut,moradabad,mumbai,muzaffarpur,mysore,nagpur,nanded,narnaul,nashik,nellore,noida,palwal,panchkula,panipat,pathankot,patiala,patna,prayagraj,puducherry,pune,raipur,rajahmundry,ranchi,rewa,rewari,rohtak,rudrapur,saharanpur,salem,secunderabad,silchar,siliguri,sirsa,solapur,sri-ganganagar,srinagar,surat,thrissur,tinsukia,tiruchirapalli,tirupati,trivandrum,udaipur,udhampur,ujjain,vadodara,vapi,varanasi,vellore,vijayawada,visakhapatnam,warangal,yamuna-nagar
Empirical Probability

Empirical Probability

Probability is the possibility that any given event will occur. Empirical probability is regarded as an objective probability, which describes the extent up to which an event has occurred in the past. Hence, it is also called the relative frequency or experimental probability. This makes empirical probability different from others. We get better results from a practical situation, as compared to a theoretical approach.

In mathematical terms, Empirical Probability is defined as the ratio of number of times a particular event occurs to the total number of trials that took place for that expected outcome to occur. 


Empirical probability depends upon how the event had occurred during the trials. The formula for Empirical probability is given below:

P(E) = Number of times an event occursTotal number of times the experiment is performed (number of trials)


Number of times an event occurs - refers to the number of times a favourable event has occurred 

Total number of times the experiment is performed (number of trials) – refers to the total number of times the event was performed

However, it is to be noted that in empirical probability, the experimental conditions may differ from one experiment to the other. This is the reason that an empirical probability is regarded as an estimate of an event from a statistical point of view.

According to a famous mathematician, Thompson, empirical probability is denoted with a prime notation. This is expressed as follows:

P′(A) = n(A)n


  • n(A) is the total number of times the event A takes place
  • n is the total number of times the experiment is done

There is a particular way to calculate empirical probability. Usually, the empirical probability is based upon the law of large numbers. If you are looking for a precise answer, you need to gather more information and then perform the entire calculation. The larger the volume of information or data, the higher is the accuracy.


Let us look at this simple example that will help you understand empirical probability better.

Eight coins are tossed in total. Frequencies of the number of tails that appeared are mentioned below. 
















Determine the probability of getting tails:

i) Less than 4 times

ii) Equal to 5 times

iii) More than 6 times


Total number of heads that occurred in this experiment = 2 + 15 + 29 + 57 + 70 + 59 + 20 + 10 + 8 = 270

i)  P (occurred tails less than 4)

As per the given table, we could see that = 2 + 15 + 29 + 57 = 103

Thus, P (tails less than 4) = 103/270 = 0.38

ii) P (occurred tails equal to 5).

From given table, the required number of cases = 59

Therefore, P (tails equal to 5) = 59/270 = 0.22

iii) P (more than 6 tails)
Total number of cases = 18
So, P (tails more than 6) = 18/270 = 0.07

NEET Related Links

NEET Exam 2024

NEET 2024 Exam Dates

NEET 2024 Exam pattern

NEET 2024 Syllabus

NEET 2024 Eligibility Criteria

NEET 2024 Application

NEET UG Counselling


NEET UG Result

NEET 2024 Cut Off

Neet 2023 Toppers List Names & Rank

Neet Result 2023 Toppers list rank cut off

Neet Answer key Live Download PDF

Neet 2023 State Toppers List

JEE MAIN Related Links

JEE Main 2024

JEE Main Rank Predictor 2024

JEE Main College Predictor 2024

JEE Main 2024 Exam Dates

JEE Main 2024 Exam pattern

JEE Main 2024 Application

JEE Main 2024 Eligibility Criteria

JEE Main 2024 Syllabus

JEE Main 2024 Physics Syllabus

JEE Main 2024 Maths Syllabus

JEE Main 2024 Chemistry Syllabus

JEE Main 2024 Admit Card

JEE Main 2024 Counselling

JEE Main marks vs rank vs percentile

JEE Advanced Result 2023 live topper list

JEE Exam Preparation - How to calculate your rank jee

JEE Maths Syllabus - Important topics and weightage

JEE Advanced Related Links

JEE Advanced 2024 Exam Dates

JEE Advanced 2024 Application

JEE Advanced 2024 Eligibility Criteria

JEE Advanced 2024 Syllabus

JEE Advanced 2024 Maths Syllabus

JEE Advanced 2024 Physics Syllabus

JEE Advanced 2024 Chemistry Syllabus

JEE Advanced Exam Result

JEE Advanced Exam Dates

JEE Advanced Registration Dates

CUET Related Links

CUET 2024 Eligibility Criteria

CUET 2024 Admit Card

CUET 2024 Exam Pattern

CUET 2024 FAQs

CUET 2024 Counselling

CUET 2024 Syllabus

CUET 2024 Result

CUET 2024 Answer Key

CUET 2024 Preparation


CUET 2024 Application Form

Talk to our expert
Resend OTP Timer =
By submitting up, I agree to receive all the Whatsapp communication on my registered number and Aakash terms and conditions and privacy policy