Probability Class 10th Notes - Free NCERT Class 10 Maths Chapter 15 Notes - Download PDF

The Class 10 Maths chapter 15 notes are a brief summary of chapter 15 in the NCERT textbook. Probability Class 10 notes will help to understand the formulas, statements, rules in detail. The CBSE Class 10 Maths Chapter 15 notes/Class 10th maths Chapter 15 notes contain previous year’s questions and NCERT TextBook pdf. NCERT Class 10 Maths chapter 15 notes contain FAQ or frequently asked questions along with a topic-wise explanation. For revision, these NCERT notes for Class 10 Maths chapter 15 are very helpful. Probability notes are important for the CBSE Exam and can be downloaded from Class 10 Maths chapter 15 notes pdf download or Probability Class 10 notes pdf download.

Additionally, students can refer to

• NCERT Solutions for Class 10 Maths Chapter 15 Probability
• NCERT Exemplar Class 10 Maths Chapter 15 Solutions Probability

Random Experiment

The experiments whose results are not definite are called random experiments. We will get different results on repeating the experiments. For example,

1. In the toss of one coin, head (H) or tail (T) will appear.

2. In a throw of one dice, 1, 2, 3, 4, 5, or 6 will appear.

3. Drawing a card out of 52 playing cards is a random experiment.

Outcomes and Sample Space

The possible results of a random experiment are called outcomes.

In one toss of a coin, head (H) or tail (T) will appear. Therefore the possible outcomes in a toss of a coin are H or T.

The set of all possible outcomes of a random experiment is called a sample space. It is denoted by S. Each element of sample space is called sample point.

In a toss of one coin, the sample space

S = {H, T}.

In a toss of two coins, the sample space

S = {HH,HT, TH, TT}

In a throw of one dice, the sample space

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

In a throw of two dice, the sample space

S = (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Event

Any subset of a sample space ‘S’ is called an event, e.g., in a toss of a coin, the sample space

S = {H, T}

If head (H) appears on the coin, it is an event. If tail (T) appears on the coin, it is another event. Both events cannot occur simultaneously.

In a toss of two coins, the sample space

S= {HH, HT, TH, TT}

All elements of the above events are the elements of the sample space S.

Types Of Events

1. Simple event: If there is only one sample element in an event, then it is called a simple elementary event, e.g., in a throw of a dice, the sample space

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

There are 6 elementary events corresponding to this sample space:

E₁ = {1}, E₂ = {2}, E₃ = {3}, E₄ = {4}, E₅ = {5}, E₆ = {6}

2. Equally likely events: If the possibility of happening of an event cannot be associated with the possibility of another event, then these events are called equally likely events.

In a toss of a coin, the occurrence of H or T is an equally likely event.

In a throw of a dice, the occurrence of 1, 2, 3, 4, 5, or 6 is equally likely events.

If the faces of dice are not the same, then the events, in this case, will not be equally likely.

3. Sure and impossible events: We know that Φ⊆ S, so the empty set represents an event. This event is called an impossible event.

Similarly S ⊆ S, so it is called a sure event.

4. Complementary events: For each event, A there exists another event A’ which is called the complementary event of A.

In set notation A’ = S - A

In a single throw of a dice,

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

If A {1, 2}, then A’ = {3, 4, 5, 6 } is the complementary event of A.

Probability

If m be the number of ways of happening an event and n be the number of ways in which events are not happening and each sample point is equally likely, then

Probability of happening of the event;

P(E)=No. of favourable outcomes of the events/Total number of outcomes

=m/(m+n)

And the probability of not happening event:

P(E')=No. of unfavourable outcomes of the event/ number of outcomes

=n/(m+n)

P(E)+P(E')= 1

P(E')=1-P(E)

Therefore, the sum of the probabilities of happening an event and not happening an event is always one.

Probability of not happening the event = 1 - Probability of happening the event.

Odds in Favour and Odds Against

If an event can happen in m ways and cannot happen in n ways, then

Odds in favour of the event = m: n

and odds against of the events = n: m

Example 1. Find the probability of getting head in a toss of one coin:

Solution: In one toss of a coin

Sample space S = {H,T}

No. of total outcomes = 2

No. of favourable outcomes = 1

Probability of getting head=No. of favourable outcomes/total outcomes

=1/2

Example 2. In a throw of dice, find the probability of

(i) getting a multiple of 3 (ii) getting a number which is not a multiple of 3

Solution: In a throw of dice

S = {1,2,3,4.5,6}

No. of possible outcomes = 6

(i) Favourable outcomes of getting multiple of 3 = {3,6}

No. of favourable outcomes of multiple of 3 = 2

And the probability of getting a multiple of 3 = 2/6=1/3

(ii) Favourable outcomes of getting a number which is not multiple of 3 = {1,2,4,5}

No. of favourable outcomes = 4

And the required probability = 4/6=2/3

Significance of NCERT Class 10 Maths Chapter 15 Notes

Probability Class 10 notes provide valuable revision material. The important topics of Class 10 CBSE Maths Syllabus covered in NCERT Class 10 Maths chapter 15 notes. For offline preparation downloaded it from Class 10 Maths chapter 15 notes pdf download or Probability Class 10 notes pdf download

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