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NCERT Solutions for Class 10 Maths Chapter 15 - Probability is curated by our team of subject experts at Toppr in a detailed manner. Probability Class 10 is made strictly in accordance with the CBSE Curriculum and the exam pattern. The NCERT textbook questions are answered in a way to provide you with a better understanding of the concepts in a systematic and step-by-step manner. It also contains the appropriate diagrams to explain the concepts to the students. As Class 10 exams are Board exams, these solutions will not only help the students in preparing for the board exams but also for the Olympiads. NCERT Solutions provided by Toppr are the best study material to excel in the exams. Also, the MCQs and long and short questions are all answered according to the weightage and the exam pattern. With the help of probability class 10 ncert solutions Maths Chapter 15 you can also test your subject knowledge and analyze your shortcomings and work on them before the exams. These are the best resources designed after proper study and research and study to help the students in scoring good marks.

Table of Content

Exercise: 15.1

Question 1

Complete the following statements:

(i) Probability of an event E + Probability of the event not E $=$ ______.

(ii) The probability of an event that cannot happen is _____. Such an event is called _____.

(iii) The probability of an event that is certain to happen is _____. Such an event is called ______.

(iv) The sum of the probabilities of all the elementary events of an experiment is _____.

(v) The probability of an event is greater than or equal to _____ and less than or equal to ______.

(i) Probability of an event E + Probability of the event not E $=$ ______.

(ii) The probability of an event that cannot happen is _____. Such an event is called _____.

(iii) The probability of an event that is certain to happen is _____. Such an event is called ______.

(iv) The sum of the probabilities of all the elementary events of an experiment is _____.

(v) The probability of an event is greater than or equal to _____ and less than or equal to ______.

Solution

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(i) Probability of event $E$ and probability of event not $E=P(E)+P(Eˉ)=1$

(ii) Probability of ab event that cannot happen is $zero (0)$, Such an event is called $Impossible Events$.

(iii) The probability of an event that is certain to happen is $1$. Such an event is called $sure or certain event$.

(iv) The sum of the probabilities of all the elementary events of an experiment is $i=1∑n P(E_{i})=1$.

(v) The probability of an event is greater than or equal to $zero(0), impossible event$ and less than or equal to $1, sure or certain event$.

Question 2

Which of the following experiments have equally likely outcomes? Explain.

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

(iv) A baby is born. It is a boy or a girl

(i) A driver attempts to start a car. The car starts or does not start.

(ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.

(iii) A trial is made to answer a true-false question. The answer is right or wrong.

(iv) A baby is born. It is a boy or a girl

Solution

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i) The car getting started or not started depends on how old the car is, is their fuel in the engine, is has met in an accident etc.

so, the factors on which the car will start or not is not the same in both cases.

Therefore,it is not an equally likely event.

iii) The answer can only be right or wrong. it is equally likely that answer is right or wrong because it is a true false question.

Therefore,it is an equally likely event.

so, the factors on which the car will start or not is not the same in both cases.

Therefore,it is not an equally likely event.

ii) The amount of shots he/she shoots can go in more times than it misses or vice-versa depending on player ability. which is not specified here.

Therefore,it is not an equally likely event.

iii) The answer can only be right or wrong. it is equally likely that answer is right or wrong because it is a true false question.

Therefore,it is an equally likely event.

iv) A baby can be boy or girl. it is equally likely that the baby is a boy or a girl.

Therefore,it is an equally likely event.

Hence, The option $(iii)$ and $(iv)$ are equally likely outcomes

Therefore,it is an equally likely event.

Hence, The option $(iii)$ and $(iv)$ are equally likely outcomes

Question 3

Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

Solution

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When a coin is tossed, there is an equally likely outcome of getting either a head or a tail, so tossing a coin is a fair way of deciding.

Question 4

Which of the following cannot be the probability of an event?

Solution

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For any event A, the probability that A will occur is a number between 0 and 1,

inclusive:

$0≤P(A)≤1$

For a sure event Probability of event is $1$

$53 =0.6<1$

$25%=10025 =0.25<1$

$0.3<1$

But $1.5>1$

Hence option A is not possible

Question 5

If P(E) = 0.05, what is the probability of "not E" ?

Solution

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$P(E)=0.05$

$P(notE)=1−0.05=0.95$

Question 6

A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out

(i) an orange flavoured candy

(ii) a lemon flavoured candy

(i) an orange flavoured candy

(ii) a lemon flavoured candy

Solution

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Let $E$ be the event of taking out a candy from bag.

**Solution(i):**

**Solution(ii):**

The bag contains only lemon flavored candies, and nothing else.

There are no orange flavored candies in the bag. Hence there is no possibility of taking out an orange candy.

Therefore, $the$ $probability$ $of$ $taking$ $out$ $an$ $orange$ $flavored$ $candy$ $=0$

The bag contains only lemon flavored candies, and nothing else.

Therefore $(No.of favorable outcomes)=(Total no.of possible outcomes)$

We know that, Probability of an event $E$, $P(E)$ $=(Total no.of possible outcomes)(No.of favorable outcomes) $

$P(E)=1$

Therefore, $the$ $probability$ $of$ $taking$ $out$ $a$ $lemon$ $flavored$ $candy$ $=1$

Question 8

It is given that in a group of $3$ students, the probability of $2$ students not having the same birthday is $0.992$. What is the probability that the $2$ students have the same birthday?

Solution

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Let $B≡$ Event that 2 students do not have same birthday

$∴P(B)=0.992$

So, probability of 2 students having same birthday $P(B)=1−P(B)$

$=1−0.992$

$=0.008$

Question 9

A bag contains 3 red balls and 5 black balls. A ball drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red ?

Solution

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Number of red balls $=3$

Number of black balls $=5$

Total number of balls $=5+3=8$

$(i)$ Probability of drawing red balls $=TotalNumberofballsNumberofredballs =83 $

$(ii)$ Probability of drawing black balls $=TotalNumberofballsNumberofblackballs =85 $

Question 10

A box contains $5$ red marbles, $8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red ? (ii) white ? (iii) not green?

Solution

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Total number of marbles in the box $=5+8+4=17$

i) P(red) = no. of red marbles/total number of marbles

P(red) $=175 $

ii) P(white) = no. of white marbles/total number of marbles

P(white) $=178 $

iii) P(green) = no. of green marbles/total number of marbles

P(green) $=174 $

P(not green) $=1−$ P(green) $=1713 $

Question 11

A piggy bank contains hundred $50p$ coins, fifty c $1$ coins, twenty c $2$ coins and ten c $5$ coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a $50p$ coin ? (ii) will not be a c $5$ coin?

Solution

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Total number of coins in the piggy bank $=100+50+20+10=180.$

i)

P($50p$ coin) $=total number of coinsnumber of 50p coins $ $=180100 $

P($50p$ coin) $=95 $

ii)

Number of $c$ $5$ coins $=10$

Number of coins which are not $c$ $5=170$

P(coin not being $c5$) $=180170 =1817 $

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Class 10 Chapter 15 – Probability explains the various ways and means to calculate the probability of the happening of an event. The chapter also focuses on the real-life problems and applications of the concept of probability. Probability is an important concept that is useful in making predictions and estimates. The chapter has a weightage of around 10 marks in the exams.
NCERT Solutions for Class 10 Maths Chapter 15 – Probability deals with different topics related to probability. These topics include that include the difference between experimental probability and theoretical probability, Why the probability of a sure event (or certain event) is 1, How the probability of an impossible event is 0, Elementary events, Complementary events and finding the probability of different events.
### Key Features of Probability NCERT Solutions Class 10 Maths Chapter 15

- Class 10 NCERT Solutions are provided in a step-by-step manner with appropriate diagrams.
- The solutions provide a better understanding of the subject and concepts.
- These are curated by the experts after thorough research.
- These solutions provide excellent study material for revision.
- They are the best means to evaluate your preparations and overcome your shortcomings.
- The Class 10 NCERT Solutions will help the students in board exams as well as Olympiads.
- These are absolutely free to download.

Related Chapters

- Chapter 1 : Real NumbersChapter 2 : PolynomialsChapter 3 : Pair of Linear Equations in Two VariablesChapter 4 : Quadratic EquationsChapter 5 : Arithmetic ProgressionChapter 6 : TrianglesChapter 7 : Coordinate GeometryChapter 8 : Introduction to TrigonometryChapter 9 : Some Applications of TrigonometryChapter 10 : CirclesChapter 11 : ConstructionsChapter 12 : Area Related to CirclesChapter 13 : Surface Areas and VolumesChapter 14 : Statistics

Question 1. State some of the applications of probability in day to day life.

Answer. Some of the applications of probability in our day to day life are:

- Drawing a card from the deck
- Flipping of coins
- Rolling a dice
- A man winning a lottery
- Picking an item from a number of items

Question 2. State the law behind probability.

Answer. The law of probability shows how likely is it for a particular occurrence to occur. The rule of large numbers states that the more trials we give to an experiment, the closer we get to a precise probability. In order to calculate the likelihood of two occurrences occurring at the same time, we use the multiplication rule.

Question 3. When can we expect the experimental and theoretical probabilities to be nearly the same?

Answer. The experimental probability of an event is based on what has actually happened. It is also known as empirical probability. The theoretical probability of the event attempts to predict what will happen on the basis of certain assumptions. As the number of trials in an experiment, goes on increasing we may expect the experimental and theoretical probabilities to be nearly the same.

Question 4. What is the probability of a certain event?

Answer. The probability of a certain event is 1.

Question 5. What is the probability of an impossible event?

Answer. The probability of an impossible event is 0.

Question 6. What is an elementary event?

Answer. 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.

Related Chapters

- Chapter 1 : Real NumbersChapter 2 : PolynomialsChapter 3 : Pair of Linear Equations in Two VariablesChapter 4 : Quadratic EquationsChapter 5 : Arithmetic ProgressionChapter 6 : TrianglesChapter 7 : Coordinate GeometryChapter 8 : Introduction to TrigonometryChapter 9 : Some Applications of TrigonometryChapter 10 : CirclesChapter 11 : ConstructionsChapter 12 : Area Related to CirclesChapter 13 : Surface Areas and VolumesChapter 14 : Statistics