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Class 11 Probability Maths Chapter 16 deals with the study of the axiomatic approach to probability with suitable examples. Class 11 Maths Chapter 16 explores the key concepts of sample space, sample points, events, and their types like impossible events, sure events and complementary events, set operations on events, mutually exclusive events and much more. Class 11 Maths Chapter 16 Probability will help students to gain a thorough understanding of this concept and its practical applications. The expert faculty of Toppr produced these solutions to assist students with their first-term exam preparations.

Class 11 Probability Chapter 16 also covers topics such as Outcomes and sample spaces, sample space and sample point definitions, event occurrence, different forms of events such as impossible, certain, complimentary, mutually exclusive events, algebra of events, and so on. The use of set theory to translate event operations and hence derive the probability of union and intersection of occurrences is also discussed. Students will quickly learn about these concepts if they practice Chapter 16 Maths Class 11 NCERT Solutions of Probability. All of these solutions have been created with the new CBSE pattern in mind, ensuring that students have a thorough understanding of their exams. It goes over all major concepts in depth, allowing students to better understand the ideas.

Chapter 16 Maths Class 11 Questions and Answers can help you get good grades in tests and properly prepare for all of the important concepts. Several examples provided in the solutions will assist students with a better understanding of Probability. Class 11 Probability NCERT Solutions Chapter 16 is available below in pdf format, and a few solutions are also included in the exercises. These solutions explain the topics covered with examples so that students can easily relate to the notion being discussed.

Table of Content

Exercise 16.1

Question 1

Describe the sample space for the indicated experiment : A coin is tossed three times

Solution

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A coin has two faces : head $(H)$ and tail $(T)$

When a coin is tossed three times the total number of possible outcomes is $2_{3}=8$

Thus when a coin is tossed three times the sample space is given by :

$S$ $={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}$

When a coin is tossed three times the total number of possible outcomes is $2_{3}=8$

Thus when a coin is tossed three times the sample space is given by :

$S$ $={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}$

Question 2

Describe the sample space for the indicated experiment : A die is thrown two times

Solution

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When a die is thrown the possible outcomes are $1,2,3,4,5$ or $6$

When a die is thrown two times the sample space is given by $S={(x,y):x,y=1,2,3,4,5,6}$

The number of elements in this sample space is $6×6=36$ while the sample space is given by :

$S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}$

When a die is thrown two times the sample space is given by $S={(x,y):x,y=1,2,3,4,5,6}$

The number of elements in this sample space is $6×6=36$ while the sample space is given by :

$S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}$

Question 3

Describe the sample space for the indicated experiment : A coin is tossed four times

Solution

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When a coin is tossed once there are two possible outcomes : Head $(H)$ and tail $(T)$

When a coin is tossed four times the total number of possible outcomes is $2_{4}=16$

Thus when a coin is tossed four times the sample space is given by :

${S=HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}$

When a coin is tossed four times the total number of possible outcomes is $2_{4}=16$

Thus when a coin is tossed four times the sample space is given by :

${S=HHHH,HHHT,HHTH,HHTT,HTHH,HTHT,HTTH,HTTT,THHH,THHT,THTH,THTT,TTHH,TTHT,TTTH,TTTT}$

Question 4

A coin is tossed and a die is thrown write the simple space.

Solution

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Now when coin is tossed and a die is rolled simultaneously, $(2×6)$ possible result =

$(Head,1),(Head,2),(Head,3),(Head,4),(Head,5),(Head,6),(Head,3),(Tail,1),(Tail,2),(Tail,3),(Tail,4),(Tail,5),(Tail,6)$

Question 5

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

Solution

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When coin is tossed, either we get head or tail.

Lets head be denoted by $H$ and tail denoted by $T$.

According to a question when head is shown then a die is rolled.

Hence,

Total number of sample space $S$ associated with the experiment

$S={H_{1},H_{2},H_{3},H_{4},H_{5},H_{6},T}$.

Question 6

$2$ boys and $2$ girls are in Room $X$ and $1$ boy and $3$ girls in Room $Y$ Specify the sample space for the experiment in which a room is selected and then a person

Solution

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Given $2$ rooms

In one room $x−2$ boys, $2$ girls

$[B_{1},B_{2},G_{1},G_{2}]$

In one room $y−1$ boy, $3$ girls

$[B_{3},G_{3},G_{4},G_{5}]$

$∴$ When room $x$ is selected, there are four probabilities of members solution

$∴$ Sample space $S={xB_{1},xB_{2},xG_{1},xG_{2},yB_{3},yG_{3},yG_{4},yG_{5}}$

Question 7

One die of red colour one of white colour and one of blue colour are placed in a bag.

One die is selected at random and rolled its colour and the number on its uppermost face is noted. Describe the sample space

One die is selected at random and rolled its colour and the number on its uppermost face is noted. Describe the sample space

Solution

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A die has six faces that are numbered from $1$ to $6$ with one number on each face.

Let us denote the red, white, and blue dices as $R,W$ and $B$ respectively.

Accordingly when a die is selected and then rolled the sample space is given by,

$S=R_{1},R_{2},R_{3},R_{4},R_{5},R_{6},W_{1},W_{2},W_{3},W_{4},W_{5},W_{6},B_{1},B_{2},B_{3},B_{4},B_{5},B_{6}$

Let us denote the red, white, and blue dices as $R,W$ and $B$ respectively.

Accordingly when a die is selected and then rolled the sample space is given by,

$S=R_{1},R_{2},R_{3},R_{4},R_{5},R_{6},W_{1},W_{2},W_{3},W_{4},W_{5},W_{6},B_{1},B_{2},B_{3},B_{4},B_{5},B_{6}$

Question 8

An experiment consists of recording boy-girl composition of families with 2 children

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

(ii) What is the sample space if we are interested in the number of girls in the family?

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

(ii) What is the sample space if we are interested in the number of girls in the family?

Solution

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When there are $2$ children in a family, they can be both boys , both girls or $1$ boy and $1$ girl

(i) When the order of the birth of a girl or a boy is considered the sample space is given by $S={GG,GB,BG,BB}$

(ii) Since the maximum number of children in each family is $2$, a family can either have $2$ girls or $1$ girl or no girl. Hence the required sample space is $S={0,1,2}$

(i) When the order of the birth of a girl or a boy is considered the sample space is given by $S={GG,GB,BG,BB}$

(ii) Since the maximum number of children in each family is $2$, a family can either have $2$ girls or $1$ girl or no girl. Hence the required sample space is $S={0,1,2}$

Question 9

A box contains $1$ red and $3$ identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment

Solution

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A box contain $1$ red and $3$ identical white balls

Let $R$ denote the red ball and $W$ denote the identical white ball

The $2$ ball selected at random in succession without replacement

Sample space is

$S={RW,WR,WW}$

$1st$ ball $2nd$ ball

$R$ $W$

$W$ $R$

$W$ $W$

Question 10

An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss then a die is rolled once. Find the sample space

Solution

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A coin has two faces: Head $(H)$ and tail $(T)$

A die has six faces that are numbered from $1$ to $6$ with one number on each face.

Thus in the given experiment the sample space is given by ,

$S=HH,HT,T1,T2,T3,T4,T5,T6$

A die has six faces that are numbered from $1$ to $6$ with one number on each face.

Thus in the given experiment the sample space is given by ,

$S=HH,HT,T1,T2,T3,T4,T5,T6$

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Practice more questions

Probability is a metric that indicates how likely an event is to occur. It is defined mathematically as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

**Outcomes**- A possible result of a random experiment is called its outcome.**Sample Space**- The set of all outcomes is called the sample space of the experiment. It serves as a universal set.

An Event in probability is a set of outcomes of any random experiment. Any subset E of a sample space S is called an event.

**Impossible and Sure Event**- 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.**Simple Event**- If event E has only one sample point of a sample space, it is called a Simple (or elementary) event.**Compound Event**- If an event has more than one sample point, it is called a Compound event.

- Probability of an event
*P(A) = n(A) / n(S)* - where, n(A) = number of elements in the set A
- n(S) = number of elements in set S
- If A and B are any two events, then
*P(A or B) = P(A) + P(B) – P(A and B)* - If A and B are mutually exclusive, then
*P(A or B) = P(A) + P(B)* - If A is any event, then
*P(not A) = 1 – P(A)*

Related Chapters

- Chapter 1 : SetsChapter 2 : Relations and FunctionsChapter 3 : Trigonometric FunctionsChapter 4 : Principle of Mathematical InductionChapter 5 : Complex Numbers and Quadratic EquationsChapter 6 : Linear InequalitiesChapter 7 : Permutations and CombinationsChapter 8 : Binomial TheoremChapter 9 : Sequences and SeriesChapter 10 : Straight LinesChapter 11 : Conic SectionsChapter 12 : Introduction to Three Dimensional GeometryChapter 13 : Limits and DerivativesChapter 14 : Mathematical ReasoningChapter 15 : Statistics

**Q1. ****How many exercises are there in Class 11 Probability NCERT Solutions****?**

**Answer:** NCERT Solutions Class 11 Probability Maths Chapter 16 consists of 44 expert-curated questions. There are 28 lengthy responses, 8 moderate questions, and 8 simple questions. Aside from these, there are 10 more questions in the miscellaneous exercise. The solutions to the exercise-specific questions are also accessible in PDF format, with the goal of assisting students in performing well in the yearly exam.

**Q2. What are the key subtopics in Class 11 Probability Maths Chapter 16 that could be tested?**

**Answer:** NCERT Solutions Class 11 Maths Chapter 16 includes definitions of sample space and sample points, events, and distinct sorts of occurrences. The algebra of events is also thoroughly investigated, as is the translation of event operations. It is not only an important lesson for exams but it is also required of students in the 12th grade. Students can now study and stay up to date on the latest CBSE syllabus by using the NCERT Solutions, which are available in PDF format.

**Q3. Is it necessary to practice all of the questions in Class 11 Probability NCERT Solutions?**

**Answer:** Class 11 Probability NCERT Solutions are well-designed to help students study basic probability concepts easily. It thoroughly covers all essential principles, allowing students to grasp the concepts. All of the exercises, examples, and practice problems have been meticulously designed to help students gain a rapid and effective comprehension of the various topics.

Related Chapters

- Chapter 1 : SetsChapter 2 : Relations and FunctionsChapter 3 : Trigonometric FunctionsChapter 4 : Principle of Mathematical InductionChapter 5 : Complex Numbers and Quadratic EquationsChapter 6 : Linear InequalitiesChapter 7 : Permutations and CombinationsChapter 8 : Binomial TheoremChapter 9 : Sequences and SeriesChapter 10 : Straight LinesChapter 11 : Conic SectionsChapter 12 : Introduction to Three Dimensional GeometryChapter 13 : Limits and DerivativesChapter 14 : Mathematical ReasoningChapter 15 : Statistics