# Probability Formula

The probability formula is used to find the probability of an event. Probability can be defined as the likelihood of an event to happen. It is the chance of pre-deciding the possibility of an event to happen. It can be calculated by probability formula by simply dividing the favorable number of outcomes by the total number of possible outcomes. The value of the probability of an event to happen can lie between 0 and 1 because the favorable number of outcomes can never cross the total number of outcomes. Also, the favorable number of outcomes cannot be negative. The probability formula along with solved examples is explained below

## What is the Probability Formula?

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,

Where,

- P(B) is the probability of an event “B”
- n(B) is the number of favorable outcomes of an event B
- n(S) is the total number of events occurring in a sample space

### Different Probability Formulas

**Probability formula with addition rule:**Whenever an event is the union of two other events, say A and B, then

P(A or B) = P(A) + P(B) − P(A∩B)

P(A ∪ B) = P(A) + P(B) − P(A∩B)**Probability formula with complementary rule:**Whenever an event is the complement of another event, specifically, if A is an event, then P(not A)=1−P(A) or P(A') = 1 - P(A').

P(A)+P(A′)=1.**Probability formula with the conditional rule**: When event A is already known to have occurred and the probability of event B is desired, then P(B, given A)=P(A and B)P(A, given B). It can be vice versa in the case of event B.

P(B∣A)=P(A∩B) ÷ P(A)**Probability formula with multiplication rule**: Whenever an event is the intersection of two other events, that is, events A and B need to occur simultaneously. Then P(A and B)=P(A)⋅P(B).

P(A∩B)=P(A)⋅P(B∣A)

Let us understand the rhombus formula better using a few solved examples.

## Examples Using Probability Formulas

**Example 1:** Find the probability of getting a face card from a standard deck of cards using the probability formula.

**Solution:** To find:

Probability of getting a face card

Given: Total number of cards = 52

Number of face cards = Favorable outcomes = 12

Using Probability Formula,

Probability = (Favorable Outcomes)÷(Total Favourable Outcomes)

P(face card) = 12/52

m = 3/13

**Answer:** The probability of getting a face card is 3/13

**Example 2**: Find the probability of getting a number less than 5 when a dice is rolled by using the probability formula.

**Solution **

To find:

Probability of getting a number less than 5

Given: Sample space = {1,2,3,4,5,6}

Getting a number less than 5 = {1,2,3,4}

Therefore, n(S) = 6

n(A) = 4

Using Probability Formula,

P(A)=(n(A))/(n(s))

p(A)=4/6

m=2/3

**Answer: The probability of getting a number less than 5 is 2/3.**

**Example 3:** What is the probability of getting a sum of 9 when two dice are thrown?

**Solution:**

There is a total of 36 possibilities when we throw two dice.

To get the desired outcome i.e., 9, we can have the following favorable outcomes.

(4,5),(5,4),(6,3)(3,6). There are 4 favorable outcomes.

Probability of an event P(E) = (Number of favorable outcomes) ÷ (Total outcomes in a sample space)

Probability of getting number 9 = 4 ÷ 36 = 1/9

**Answer:** Therefore the probability of getting a sum of 9 is 1/9.

## FAQs on Probability Formulas

### How To Calculate Probability Using the Probability Formula?

The probability of any event depends upon the number of favorable outcomes and the total outcomes. In general, probability is the ratio of the number of favorable outcomes to the total outcomes in that sample space. It is expressed as, Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

### Where Do We Use the Probability Formula In Our Real Life?

The following activities in our real-life tend to follow the probability formula:

- Weather forecasting
- Playing cards
- Voting strategy in politics
- Rolling a dice.
- Pulling out the exact matching socks of the same color
- Chances of winning or losing in any sports.

### How To Determine Probability Using Probability Formula?

The probability can be determined by figuring out the total number of outcomes of that respective event. A probability is generally calculated for an event (x) within the total number of outcomes of the given sample space. The probability of happening an event is the ratio of the number of outcomes of an event to the total number of possible outcomes or sample space. The probability formula is given as Probability of an event P(E) = (Number of favorable outcomes) ÷ (Number of events in the sample space).

### What Is the Conditional Probability Formula?

The conditional probability depends upon the happening of one event based on the happening of another event. The conditional probability formula of happening of event B, given that event A, has already happened is expressed as P(B/A) = P(A ∩ B)/P(A).