#### Topics

##### Sets and Relations

##### Functions

##### Complex Numbers 33

##### Sequences and Series

##### Locus and Straight Line

##### Determinants

##### Limits

##### Continuity

##### Differentiation

##### Partition Values

##### Measures of Dispersion

##### Skewness

##### Bivariate Frequency Distribution and Chi Square Statistic

##### Correlation

##### Permutations and Combinations

- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Concept of Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Concept of Combinations
- Properties of Combinations

##### Probability

##### Linear Inequations

##### Commercial Mathematics

#### description

- Simple or elementary event
- Occurrence and non-occurrence of event
- Sure Event
- Impossible Event
- Complimentary Event

#### notes

Events can be classified into various types on the basis of the elements they have.**i) Impossible and Sure Events:**

The empty set φ and the sample space S describe events. In fact φ is called an impossible event and S, i.e., the whole sample space is called the sure event.

To understand these let us consider the experiment of rolling a die. The associated sample space is

S = {1, 2, 3, 4, 5, 6}

Let E be the event “ the number appears on the die is a multiple of 7”. Can you write the subset associated with the event E? Clearly no outcome satisfies the condition given in the event, i.e., no element of the sample space ensures the occurrence of the event E. Thus, we say that the empty set only correspond to the event E. In other words we can say that it is impossible to have a multiple of 7 on the upper face of the die. Thus, the event E = φ is an impossible event. **ii) Simple Event:**

If an event E has only one sample point of a sample space, it is called a simple (or elementary) event.

In a sample space containing n distinct elements, there are exactly n simple simple events.

For example in the experiment of tossing two coins, a sample space is S={HH, HT, TH, TT}

There are four simple events corresponding to this sample space. These are `E_1= {HH}, E_2={HT}, E_3= { TH} and E_4={TT}.`

**iii) Compound Event:**

If an event has more than one sample point, it is called a Compound event.

For example, in the experiment of “tossing a coin thrice” the events

E: ‘Exactly one head appeared’

F: ‘Atleast one head appeared’

G: ‘Atmost one head appeared’ etc.

are all compound events. The subsets of S associated with these events are E={HTT,THT,TTH}

F={HTT,THT, TTH, HHT, HTH, THH, HHH}

G= {TTT, THT, HTT, TTH}

Each of the above subsets contain more than one sample point, hence they are all compound events.