## Probability in Aptitude – Definition, Formula, Types, Problems and solutions

This is aptitude questions and answers section on Probability with explanation for various interview, competitive examinations and entrance tests.

## Probability Formula

**The formula of the probability of an event is**:

**P(A) = n(A)/n(S)**

Where,

- 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

**Note:** Here, the favourable outcome means the outcome of interest.

Sometimes, students get confused about the word “favourable outcome” with “desirable outcome”. 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.

students of class 10 can solve Probability class 10 mcq with these formula . students of class 9 can also solve Probability class 9 mcq with these formula

### Probability Formulas

Let A and B are two events. The formulas are listed below:

Probability Range | 0 ≤ P(A) ≤ 1 |

Rule of Addition | P(A∪B) = P(A) + P(B) – P(A∩B) |

Rule of Complementary Events | P(A’) + P(A) = 1 |

Disjoint Events | P(A∩B) = 0 |

Independent Events | P(A∩B) = P(A) ⋅ P(B) |

Conditional Probability | P(A | B) = P(A∩B) / P(B) |

Bayes Formula | P(A | B) = P(B | A) ⋅ P(A) / P(B) |

## What is probability ?

Let’s move and learn something more about probability, it’s rules and test questions and examples.

##### Rule 1

The first rule of probability reflects to very basics of the topic. It informs us that the likelihood of an event lie between 0 and 1. In that case, 0 means that the chances of the event to occur is not possible. While 1 denotes that chances of the event to occur is maximum.

In other words, the probability of an outcome A, denoted as P (A) , is a number between 0 and 1 indicating the proportion of the time that the outcome A occurs in the long span of time. For instance, when the probability of an event is close to 0, it’s occurrence is unlikely. If the probability of an event is 0.5, there is about 50% chance that the event will occur, and when the probability of an event is close to 1, the event is highly likely to occur.

This is denoted by 0<= P (A) <=1

##### Rule 2

The sum of the probabilities of all the possible outcomes is 1. For instance, in rolling a single dice, each outcome in the sample space has a probability of ⅙, and the total of all outcomes equal to 1.

##### Rule 3

If an event A cannot occur i.e., the event contains no members in the sample space, it’s probability is 0. For instance, when a single dice is rolling, what can be the probability of getting a number greater than 6. Since all the sample spaces are 1,2,3,4,5 and 6. As it is seen that all the space is less than 6. So, the probability of getting a number more than 6 is zero i.e., not possible.

##### Rule 4

If an event A is certain, then it’s probability is 1. For instance, when a a single dice is rolling, then what shall be the probability of getting a number less than 8. Since all the outcomes are 1,2,3,4,5 and 6. As it is seen that all the outcomes are less than 8. So, the probability is 1.

P (number less than 8) = 6/6 = 1 or 100%

Then event of number getting less than 8 is certain.

##### Rule 5

The Complement Rule states that the sum of the probabilities of an event and its complement must equal 1.

P(A)+P(A′)=1

So, P (A’) = 1 – P (A)