from a handpicked tutor in LIVE 1-to-1 classes

# Probability Formulas Class 12

Despite the fact that the probability formulas class 12 are simple, students may struggle to memorize them due to the lack of conceptual understanding. Hence, this article covers all the main probability formulas class 12 and their examples for students to understand them easily. Additionally, there are some helpful tips that, if followed properly, will assist students in memorizing formulas better.

## List of Probability Formulas Class 12

Students can refer to the list of probability formulas class 12 provided below:

**Conditional Probability:**The conditional probability of an event E, given the occurrence of the event F is: P(E | F) = P(E ∩ F)/P(F) where P(F) ≠ 0

**Properties of Conditional Probability:**

There are three main properties of conditional probability as explained below:

**i) Property 1:**If E and F are the events of a sample space say S, P(S|F) = P(F|F) = 1**ii) Property 2:**If A and B are two events in a sample space S and F is an event of S such that P(F) ≠ 0, P((A ∪ B)|F) = P(A|F) + P(B|F) – P((A ∩ B)|F).

**iii) Property 3:** P(A′|B) = 1 − P(A|B)

**Multiplication Theorem on Probability**: If E and F are independent, then P (E ∩ F) = P (E) P (F)

P (E|F) = P (E), P (F) ≠ 0

P (F|E) = P (F), P(E) ≠ 0

**Theorem of Total Probability:**Let {E1, E2, ...,En) be a partition of a sample space and suppose that each of E1, E2, ..., En has a nonzero probability. Let A be any event associated with S, then P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En)**Bayes' theorem:**Bayes’ theorem describes the probability of an event based on prior knowledge of the conditions that might be relevant to the event. The formula to determine the conditional probability of an events P(A|B) = [ P (B|A) x P(A) ] / P(B), Where P(A|B) is the probability of an event A that is occurring when event B has occurred,

P(B|A) is the probability of an event B that is occurring when event A has occurred and P(A) is the probability of event A; P(B) is the probability of event B

## Applications of Probability Formulas Class 12

Conditional probability finds its place in various aspects of life. Here are a few applications of probability formulas class 12:

- Conditional Probability formulas for class 12 are useful in finding solutions to problems in the field of medical science, weather forecasting, etc.
- These formulas are also applicable in marketing and finance to predict the financial trends related to stock markets.
- Probability formulas class 12 are applied to set the insurance value and predict various other factors.

## Probability Formulas Class 12 Examples

**Example:** Twenty cards numbered 1 to 20 are placed in a jar, and one card is drawn randomly. Considering the number on the drawn card is more than 4, what would be the probability of the number on the card drawn to be even?

**Solution:** Let X be the event as ‘number on the card is even’ and Y be the event ‘number on the card is greater than 4’.

Sample space of this experiment is,

S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ,11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

We need to find P(X|Y)

X = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

Y = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

X ∩ Y = {6, 8, 10,12, 14, 16, 18, 20}

Also,

P(X) = 10/20

P(Y) = 16/20

P(X∩Y) = 8/20

Then P(A|B) = P(A∩B)/ P(B)

= 8/20 * 20/16 = 8/16 = 1/2

## Tips to Memorize Probability Formulas Class 12

Here are some tips that students can apply to memorize the Probability formulas class 12 easily:

- The first step in learning probability is to clear all basics. Students should practice the exercise questions only after gaining a precise knowledge of concepts.
- Students must practice a lot of problems related to probability in their textbooks to gain a deep understanding of the practical use of these formulas.
- Students can use formula images as wallpaper on their desktops and mobile devices by downloading them. Hence, every time they use these devices, they will be able to do a quick revision.

Students can download the printable **Maths Formulas Class 12** sheet from below.

## FAQs on Probability Formulas Class 12

### What are the Important Probability Formulas Class 12?

The important Probability Formulas Class 12 are:

- The conditional probability of an event E, given the occurrence of the event F is given by P(E | F) = P(E ∩ F)/P(F) where P(F) ≠ 0
- 0 ≤ P (E|F) ≤ 1
- P (E′|F) = 1 – P (E|F)
- P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0

P (E ∩ F) = P (F) P (E|F), P (F) ≠ 0

- If E and F are independent, then P (E ∩ F) = P (E) P (F)

P (E|F) = P (E), P (F) ≠ 0

P (F|E) = P (F), P(E) ≠ 0

- Theorem of Total probability: P(A) = P(E1 ) P (A|E1 ) + P (E2 ) P (A|E2 ) + ... + P (En ) P(A|En )
- Baye’s Theorem: P(A|B) = P(B|A)P(A)/P(B);

### Where P(A|B) is the probability of an event A that is occurring when event B has occurred

P(B|A) is the probability of an event B that is occurring when event A has occurred

P(A) is the probability of event A; P(B) is the probability of event.

### What are the Basic Formulas in Probability Formulas Class 12?

The basic formulas in probability formula class 12 will help students understand the theory of conditional probability, independent events, mean and variance of random variables. Also, they will learn about Baye's theorem and Bernoulli trials.

### What are the Important Formulas Covering Probability Formulas Class 12?

The important formulas covering Probability Formulas Class 12 are related to conditional probability, its properties, multiplication theorem, Bayes’ Theorem, independent events, random variables and their probability distributions, mean/variance of a random variable, Binomial distribution and Bernoulli trials.

### How Many Formulas are There in Probability Formulas Class 12?

There are around five basic formulas in probability formulas class 12 that the students can find in this article. To learn them properly it is essential to go through the solved examples in the textbooks. This article also has some useful tips that will help students in remembering these formulas.

### How can I memorize Probability Formulas Class 12?

Some tips that will help students to memorize Probability formulas class 12 easily are:

**Solved Problems:** Students must make an attempt to solve all the problems and sample questions provided in their textbooks to understand the practical use of the formulas.

**Group study:** Studying together will help students to learn and share their knowledge with their friends. And also it will help them know about the different problem-solving strategies.

**Formula images:** Applying formula images as wallpapers on mobiles can help students revise them easily.

visual curriculum