Class 11 Maths Probability | Events |

**Event**: It is the set of favorable outcome. Also, Event is a subset of the sample space. E.g. Event of getting odd outcome in a throw of a die

Types of Event

- Impossible and Sure Events
- Simple Event
- Compound Event

Impossible event is denoted by φ, while Sure Event is denoted by S.

E.g. in rolling a die, impossible event is that number is more than 6 & Sure event is the event of getting number less than or equal to 6.

Simple Event has only one sample point of a sample space.

E.g. in rolling a die, Simple event could be the event of getting 4.

Compound Event has more than one sample points of a sample space.

E.g. in rolling a die, Simple event could be the event of getting even number

**Algebra of Events**

- Complementary Event
- Event ‘A or B’
- Event ‘A and B’
- Event ‘A but not B

**Complementary Event**

Complementary event to A= ‘not A’

Example: If event A= Event of getting odd number in throw of a die, that is {1, 3, 5}

Complementary event to A = Event of getting even number in throw of a die, that is {2, 4, 6}

Or A’ = S- A (where S is the Sample Space)

**Event (A or B)**

Union of two sets A and B denoted by A ∪ B contains all those elements which are either in A or in B or in both.

When the sets A and B are two events associated with a sample space, then ‘A ∪ B’ is the event ‘either A or B or both’. This event ‘A ∪ B’ is also called ‘A or B’.

Event ‘A or B’ = A ∪ B = {ω : ω ∈ A or ω ∈ B}.

**Event ‘A and B’ **

Intersection of two sets A ∩ B is the set of those elements which are common to both A and B. i.e., which belong to both ‘A and B’.

If A and B are two events, then the set A ∩ B denotes the event ‘A and B’.

Thus, A ∩ B = {ω : ω ∈ A and ω ∈ B}

**Event ‘A but not B’**

A–B is the set of all those elements which are in A but not in B. Therefore, the set A–B may denote the event ‘A but not B’. A – B = A ∩ B’

**Mutually exclusive events**

Events A and B are called mutually exclusive events if occurrence of any one of them excludes occurrence of other event, i.e., if they cannot occur simultaneously.

Example: A die is thrown. Event A = All even outcome & event B = All odd outcome. Then A & B are mutually exclusive events, they cannot occur simultaneously.

**Exhaustive events**

Lot of events that together forms sample space. Example: A die is thrown. Event A = All even outcome & event B = All odd outcome. Even A & B together forms exhaustive events as it forms Sample Space.

.