## Unit: 18

__Probability__

Before starting the discussion about Probability we have to review the following concept.

### 18.1 Definitions of basic terms on probability – Review

**(i) Random experiments**

Any experiment whose outcome cannot be predicted or determined in advance is called a random experiment. For example, tossing a coin, rolling a die, etc are random experiments.

**(ii) Outcomes**

The results of a random experiment are called outcomes. For example, while tossing a coin, the occurrence of head or tail is the outcome.

**(iii) Sample space**

The set of all possible outcomes of a random experiment is known as sample space. Usually, it is denoted by S. For example,

When a coin is tossed, S = {H, T}

When a die is thrown, S = {1, 2, 3, 4, 5, 6}

**(iv) Event**

A subset of the sample space S related to an experiment is known as event.

For example,

While tossing a coin 3 times. S={ HHH, HHT, HTH, HTT, THH, THT, TTH TTT }

Let A= {HHH, HHT, HTH, THH}, then, A is the event in which at least two heads are obtained.

**(v) Exhaustive cases**

The total number of all possible outcomes of a random experiment is known as exhaustive cases. For example,

While tossing a coin, S = {H, T}

So, exhaustive cases = 2 While tossing two coins simultaneously.

S={HH, HT, TH, TT}

So, exhaustive cases = 4.

#### (vi) Favourable cases

The outcomes in an random experiment which are desirable (or expected) to us are called favourable cases. For example,

While tossing a coin, S= (H, T)

Here, the favourable number of case of head is 1 and tail is also 1.

The favourable number of cases of getting a ‘king’ when a card is drawn from a well shuffled pack of 52 cards is 4.

#### (vii) Equally likely events

Two or more events are said to be equally likely if the chance of occurring any one event is equal to the chance of occurring other events. For example, while throwing a die, the chance of coming up the numbers 1 to 6 is equal. So, they are equally likely events.

#### (viii) Independent events

Two or more events are said to be independent if the occurrence or none-occurrence of one of the events does not affect the occurrence or none-occurrence of the other events. For example, in the random experiment of tossing a coin twice or more, the occurrence of any one event in the first trial does not affect the occurrence of any other event in the second trial. So, they are independent events.

#### (ix) Dependent events

Two or more events are said to be dependent if the occurrence of one of the events affects the occurrence of the other events. For example, while drawing a ball in two successive trials from a bag containing 2 red and 3 blue balls without a replacement. getting any one coloured ball in the first trial affects to get other coloured ball in the second trial. So, these are the dependent events.

#### (x) Mutually exclusive events

Two ore more events of a sample space S are said to be mutually exclusive if the occurrence of any one event excludes the occurrence of the other events. For example, while tossing a coin, the occurrence of head excludes the occurrence of tail or vice versa. So, they are mutually exclusive events. Furthermore, let’s consider the experiment of throwing a die. Let A be the event, the number obtained is even.

## Probability Class 10 Mathematics Solution PDF

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## Is Class 10 Math Guide Helpful For Student ?

I have published this Notes for helping students who can’t solve difficult maths problems. Student should not fully depend on this note for doing all exercises. If you totally depend on this note and simply copy a to z then it may affect your study.

Student should also try to solve some problems themselves. You can use this note as a reference. You should check all the answers carefully because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

## How to secure good marks in Mathematics ?

As, you may know I’m also a student. Being a student is not so easy. You have to study and work hard in 8 different subjects. From my point of view most of the student are weak in mathematics. They face difficulties while solving maths problems. I was also facing the same problem when I was in grade 10.

If you also want to secure good marks in mathematics then you should practise them everyday. You should always start your practise from a simple problems. When you solve some simple problems then it will motivates you to solve some other harder problem. Slowly and gradually increase the difficulty of questions day by day.

Maths is not only about practising. You also needs to be clear about the concept of solving the problems. When you get the concept then you can easily solve maths problems which are in similar formats.

You should make the habit of making side notes. It means you should make notes of formulas, tips of solving that problems and the main concept.

When your teacher tries to make the concept clear by giving some random example then all student tries to remember the same example but you shouldn’t do that. You should try to relate that concept with your daily life and create your own formula of remembering the concepts.

If you give proper time for your practise with proper method of practising then you’ll definitely score a good marks in your Exam. You can also make a time table for your study and read accordingly.

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Can please provide the notes of trigonometry 🙏 please

It's urgent