# Basics Of Probability -Mathematics Notes For CTET Exam: Free PDF

Mathematics is an equally important section for CTET, MPTET, KVS & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt.

To let you make the most of Mathematics section, we are providing important facts related to the Simplification. At least 1-2 questions are asked from this topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

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## PROBABILITY

Probability: It is the numerical measurement of the degree of certainty. There are two types of approaches to study probability

Experimental or Empirical Probability: The result of probability based on the actual experiment is called experimental probability. In this case, the results could be different if we do the same experiment again.

Probability — A Theoretical Approach: In the theoretical approach, we predict the results without performing the experiment actually. The other name of theoretical probability is classical probability.

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Probability of Occurrence of an Event

Theoretical probability associated with an event E is defined as “If there are ‘n’ elementary events associated with a random experiment and m of these are favourable to the event E then the probability of occurrence of an event is defined by P(E) as the ratio mn “.

If P(E) = 1, then it is called a ‘Certain Event’.

If P(E) = 0, then it is called an ‘Impossible Event’.

The probability of an event E is a number P(E) such that: 0 ≤ P(E) ≤ 1

An event having only one outcome is called an elementary event. The sum of the probabilities of all the elementary events of an experiment is 1.

For any event E, P(E) + P(E¯) = 1, where E¯ stands for ‘not E’. E and E¯ are called complementary events.

Favourable outcomes are those outcomes in the sample space that are favourable to the occurrence of an event.

### Sample Space:

A collection of all possible outcomes of an experiment is known as sample space. It is denoted by ‘S’ and represented in curly brackets.

#### Examples of Sample Spaces:

A coin is tossed = Event

E1 = Getting a head (H) on upper face

E2 = Getting a tail (T) on upper face

S = {H, T}

Total number of outcomes = 2

Two coins are tossed = Event = E

E1 = Getting a head on coin 1 and a tail on coin 2 = (H, T)

E2 = Getting a head on both coin 1 and coin 2 = (H, H)

E3 = Getting a tail on coin 1 and a head on coin 2 = (T, H)

E4 = Getting a tail on both, coin 1 and coin 2 = (T, T)

S = {(H, T), (H, H), (T, H), (T, T)}.

Total number of outcomes = 4

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### Important Note:

Coin: A coin has two faces termed as Head and Tail.

Dice: A dice is a small cube which has between one to six spots or numbers on its sides, which is used in games.

Cards: A pack of playing cards consists of four suits called Hearts, Spades, Diamonds and Clubs. Each suite consists of 13 cards.

Example 1.  A coin is tossed 10 times and the outcomes are observed as:

H, T, H, T, T, H, H, T, H, H (H is Head; T is Tail)

What is the probability of getting Head?

Ans.(a)

Sol. Probability of Getting Head

Example 2. A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is not red?

Ans.(a)

Sol.

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Example 3. Which of the following statement is incorrect?

(a) Probability of an event lies between 0 and 1.

(b) Probability of an impossible event is 1 and that of a sure event is 0.

(c) Probability is the measure of the chance of an event happening.

(d) None of these

Ans.(b)

Sol. correct statement ⟹ Probability of an impossible event is 0 and that of a sure event is 1.