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Probability Formula: Check Definition and Formulas Here


Probability Formula: The probability of an event occurring is defined by probability. There are various probability formulas that students need to keep in mind in order to have a proper understanding of the concept. Probability has numerous applications in games, in business to create probability-based forecasts, and in this new area of artificial intelligence. By dividing the favourable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be estimated using the Probability Formula.

Students can find steps on how to calculate probability formulas from this article. Some of the probability formulas which are discussed are probability range, conditional probability formula, Bayes theorem formula and so on. Students can get a clear idea of the concept and it will help them ace their exams. To know more about probability formulas, continue to read the article.

Probability Formula: Calculate Probability

Students looking for the Bayes theorem formula, Conditional probability formula, Bayes theorem formula, Conditional probability formula, and the Poisson distribution formula can check the details below.

The uncertainty/certainty of the occurrence of an event is measured by probability. Though probability started with gambling, it is now used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. Probability for Class 10 is an important chapter for students and it explains all the basic concepts.

To find the probability of a single event occurring, first, we should know the total number of possible outcomes. For example, when we toss a coin, either we get a Head or a Tail, i.e. only two possible outcomes are possible (H, T). If we want Head to come, our favourable outcome is H. So, we denote the probability of getting Head on the toss of a coin as:

Probability Formula

= 1/2

How to Calculate Probability?

The probability formula gives the possibility of an event which is about to happen. It is equal to the ratio of the number of favourable outcomes and the total number of outcomes. We have provided probability formulas with examples.

Probability of Event to Happen P(E) = Number of Favourable Outcomes/Total Number of Outcomes


Probability of Event to Happen Formula

P(A) is the probability of an event “A”
n(A) is the number of favourable outcomes
n(S) is the total number of events in the sample space

We use two terms – “favourable outcome and “desirable outcome” in the context of probability. Sometimes, students get confused between these two terms. In some of the requirements, losing in a certain test or occurrence of an undesirable outcome can be a favourable event for the experiments run.

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Basic Probability Formulas: Conditional Probability Formula, Bayes Theorem Formula

Here we have provided some of the probability math formulas that will be very helpful for students:

Probability Range0 ≤ P(A) ≤ 1
Rule of Complementary EventsP(Ac) + P(A) = 1
Rule of AdditionP(A∪B) = P(A) + P(B) – P(A∩B)
Disjoint Events – Events A and B are disjoint ifP(A∩B) = 0
Conditional ProbabilityP(A|B) = P(A∩B) / P(B)
Bayes FormulaP(A|B) = P(B|A) ⋅ P(A) / P(B)
Independent Events – Events A and B are independent iffP(A∩B) = P(A) ⋅ P(B)
Cumulative Distribution FunctionFX(x) = P(X ≤ x)

Apart from these probability formulas in Class 10, there are some other important probability equations:

Probability Mass Function

The probability mass function (PMF) (or frequency function) of a discrete random variable X assigns probabilities to the possible values of the random variable.

 probability mass function
 probability mass function formula

Furthermore, if A is a subset of the possible values of X, then the probability that X takes a value in A is given by:

Probability Density Function

The probability density function (PDF), denoted by f, of a continuous random variable X satisfies the following:

Probability Density Function


Covariance is a measure of the joint variability of two random variables. The following formula denotes it:



covx, y = covariance between variable a and y

xi = data value of x

yi = data value of y

= mean of x

ȳ = mean of y

N = Number of data values

Download – Probability Formulas PDF

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Solved Examples on Probability Formulas Class 12

Here we have provided some probability solved examples.

Question 1: A coin is thrown 3 times. What is the probability that at least one head is obtained?

Solution: Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8.
Favourable Cases = 7 [Need at least 1 Head]
P (A) = No. of Favourable Outcomes/Total number of outcomes
= 7/8

Question 2: Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.

Solution: Total no. of ways = 52C2
Case I: Both are diamonds = 13C2
Case II: Both are kings = 4C2 
P (both are diamonds or both are kings) = (13C2 + 4C2 ) / 52C2 = 14/221

Question 3: Calculate the probability of getting an even number if a dice is rolled.

Solution: Sample space (S) = {1, 2, 3, 4, 5, 6}
n(S) = 6
Let “E” be the event of getting an odd number, E = {2, 4, 6}
n(E) = 3
So, the Probability of getting an odd number is:
P(E) = (Number of outcomes favorable)/(Total number of outcomes)
= n(E)/n(S)
= 3/6
= 1/2

Question 4: What is the probability of getting a sum of 22 or more when four dice are thrown?

Solution: Total number of ways = 64 
= 1296
(i) Number of ways of getting a sum 22 are 6,6,6,4 = 4! / 3!
= 4 and 6,6,5,5 = 4! / 2!2!
= 6.
(ii) Number of ways of getting a sum 23 is 6,6,6,5 = 4! / 3! = 4
(iii) Number of ways of getting a sum 24 is 6,6,6,6 = 1.
Fav. Number of cases = 4 + 6 + 4 + 1 = 15 ways.
P (getting a sum of 22 or more) = 15/1296
= 5/432

Question 5: Find the probability that a leap year has 52 Sundays.

Solution: A leap year can have 52 Sundays or 53 Sundays.
In a leap year, there are 366 days out of which there are 52 complete weeks & the remaining 2 days.
Now, these two days can be (Sat, Sun), (Sun, Mon), (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat).
So there are a total of 7 cases out of which (Sat, Sun) (Sun, Mon) are two favourable cases.
So,  P (53 Sundays) = 2 / 7
Now, P(52 Sundays) + P(53 Sundays) = 1
So, P (52 Sundays) = 1 – P(53 Sundays) = 1 – (2/7) = (5/7)

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Practice Questions on All Probability Formulas

Here we have provided some of the practice questions for probability formulas for Class 7 for you to practice:

Question 1: Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red & 6 black balls respectively. 1 of the bags is selected at random and a ball is drawn from it. If the ball drawn is red, find the probability that it is drawn from the third bag.

Question 2: Fifteen people sit around a circular table. What are the odds against two particular people sitting together?

Question 3: From a pack of cards, three cards are drawn at random. Find the probability that each card is from a different suit.

Question 4: Two dice are thrown together. What is the probability that the number obtained on one of the dice is multiple of the number obtained on the other dice?

Question 5: 1 card is drawn at random from the pack of 52 cards.
(i) Find the probability that it is an honour card.
(ii) It is a face card.

Question 6: There are 5 green and 7 red balls. Two balls are selected one by one without replacement. Find the probability that the first is green and the second is red.

Question 7: Consider another example where a pack contains 4 blue, 2 red and 3 black pens. If a pen is drawn at random from the pack, replaced and the process repeated 2 more times, What is the probability of drawing 2 blue pens and 1 black pen?

Question 8: In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?

Frequently Asked Questions

Here we have provided some of the frequently asked questions related to statistical probability formulas:

Q1: Where can I download probability formulas for aptitude?
Ans: You can download the probability formulas for aptitude PDF from Embibe. We have provided all the basic formulas along with probability equations on this page.

Q2: Which platform is best for beginners to learn probability basics?
Ans: Embibe is one of the best education technologies that offer basic to next-level probability tutorials for students. Students can also take get access to the list of all probability formulae on Embibe and try some mock tests to be ready for their exams. 

Q3: What is the easiest way to understand probability?
Ans: The easiest way to understand probability is to first take a look at the solved question papers and the probability examples. After that, students should start with the basics of probability. There are many mock tests available on Embibe for the probability that students can attempt to clear their doubts about probability. 

Q4: What is the formula of probability?
Ans: The probability of an event is the number of favourable outcomes divided by the total number of outcomes possible. This basic definition of probability assumes that all the outcomes are equally likely to occur.

Q5: What are the 3 types of probability?
Ans: There are 3 types of probability:
(i) Theoretical Probability.
(ii) Experimental Probability.
(iii) Axiomatic Probability.

Q6: What does P (AUB) mean?
Ans: P(A U B) is the probability of the sum of all sample points in A U B. It is defined by P(A) + P(B), which is the sum of probabilities of sample points in A and in B.

Q7: What does P (A|B) mean?
Ans: P(A|B) is the conditional probability. It is the probability of event A occurring, given that event B occurs.

Practice Probability Questions with Hints & Solutions