NCERT Solutions for Class 10 Maths Chapter 15 Probability (Ex 15.1)
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Mathematics in Class 10 might be a challenging subject, but with the appropriate guidance, it can be an interesting and engaging experience. On the other hand, it is a wonderful subject that students might take interest in while studying.With a thorough understanding of the fundamentals and regular practice, mathematics may be a very simple subject to perform well in. Algebra, Coordinate Geometry, Circles, Quadratic equations, Vectors, Probability, and many other topics are part of the academic curriculum of Class 10 Mathematics. These topics can be conveniently studied with the help of NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1, which are available on the Extramarks Learning App and website.
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ToggleNCERT Solutions for Class 10 Maths Chapter 15 Probability (Ex 15.1) Exercise 15.1
A number of advantages are offered to students by the National Council of Educational Research and Training (NCERT), which was established in 1961.
In digital learning resources referred to as NCERT Solutions, all of the questions and answers from the NCERT textbooks, starting from Class 6 through Class 12, are included. These solutions, for instance, NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 might be quite helpful and practical for students during their preparation for the examinations.
Probability is a branch or tool of Mathematics that deals with the likelihood of an event occurring. There are different types of probabilities, and each one is calculated in a different way. It is expressed as a number between 0 and 1, with 0 meaning that the event will not happen and 1 meaning that the event is certain to happen. Probability can be used to calculate the possibility of two or more events occurring together or to determine the chances that a particular outcome will occur.
Probability is an important topic in Mathematics and is used in many different ways. It is significant to understand the different types of probabilities and how to calculate them. This can become easy if students utilise the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 provided on Extramarks.
It is highlyrecommended that students use the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 engineered by Extramarks, for efficient practise and effective revision. Students who use these NCERT Solutions for Class 10 Maths Chapter 15 Exercise 15.1 will have a better understanding of the subject of mathematics and the application of probability concepts in real life.
Access NCERT Solutions for Class 10 Maths Chapter 15 – Probability
Accessing the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 can help students in enhancing their Mathematical skills to solve problems effectively. The NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 are recommended by Extramarks to equip students’ examination preparation with excellent solutions. Similarly, NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 aids students in fully comprehending concepts of Probability in Mathematics with direct help from qualified mentors. The NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 must be used by students as they study and get ready for their CBSE Board examinations. The fact that the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 provide students with a comprehensive understanding of the topics covered in the Mathematics NCERT textbook is to their advantage.
Students can find comprehensive solutions with the aid of the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1. Extramarks greatly recommends the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1. These solutions are accompanied by a considerable number of unanswered questions, sample papers, and past years’ papers that will help students prepare for their examinations sufficiently.
Exercise 15.1 Class 10 NCERT Solutions Free PDF
Many students might find it demanding to be required to practise the Class 10 Maths Chapter 15 Exercise 15.1 questions on a routine basis, but with some preparation and strategy, these can be simple to complete.
Extramarks provides support to students for the academic curriculum of schools which are affiliated with the CBSE Board. The Class 10 Maths Chapter 15 Exercise 15.1 Solutions are presented in both offline and online versions, and they offer accurate solutions for the questions and test preparation.
The NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 are available on Extramarks for students. The Extramarks educational website is one of the best e-learning sites to access quality learning assets like the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 which are also available on the Extramarks mobile application. Students may acquire the Exercise 15.1 Class 10 Solutions by exploring the Extramarks website or by downloading the Extramarks Learning App.
Chapter 15 Maths Class 10 Exercise 15.1 Question 1
In Exercise 15.1, the first question is about filling in or completing the statements with appropriate answers. All five sub-questions of Question 1 ask about the Probability of the events in certain scenarios.
Exercise 15.1 Maths Class 10 PDF Question 2
According to Question 2 of Exercise 15.1, students are asked about the equally likely outcomes of the experiments or situations. There are in total 4 sub-questions in Question number 2.
Exercise 15.1 Class 10 Maths NCERT Solutions Question 3
In Question 3 of Class 10 in Exercise 15.1, the probabilities involved in tossing a coin before a Football match are asked of students. The probability of who is going to win the toss and get the ball in the Football match is calculated. Such questions can be solved by using NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1.
Maths Class 10 Chapter 15 Exercise 15.1 Question 4
In the Class 10 textbook of Mathematics, Question 4 in Exercise 15.1 asks students how the numbers or fractions given as the sub-part of the question, cannot be the probability of an event. There are 4 sub-parts of Question number 4.
Class 10 Maths Chapter 15 Exercise 15.1 Solutions Question 5
In Exercise 15.1, the fifth question demands what the probability of the alphabet E is, in the equation P(E) = 0.05. These kinds of questions can be easily solved with the help of NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 provided by Extramarks on their website.
Ex 15.1 Class 10 Question 6
Question six of Exercise 15.1 asks what is the probability of taking out an orange candy or a lemon candy by Malini without looking into the bag, from among a number of bags.
Exercise 15.1 Class 10 Question 7
In accordance with Question 7 of Exercise 15.1, students are asked about the probability of 2 students having the same birthday if the whole group includes 3 students. It is also given that the probability of 2 students not having the same birthday is 0.992.
15.1 Class 10 Question 8
As a part of the eighth question of Exercise 15.1 in Class 10, the probability of drawing a ball in a red colour or not is asked by students. There are in total 8 balls of which 3 are red balls and 5 are black balls.
Ex 15.1 Class 10 NCERT Maths Question 9
Question 9 of Exercise 15.1 is similar to Question 8. In Question 9, students are asked about the Probability of marble taken out that is either red, not green, or white colour, given that there are 17 marbles in total, 5 red marbles, 8 white marbles, and 4 green marbles.
Class 10 Maths Chapter 15 Exercise 15.1 Question 10
Question 10 of Exercise 15.1 of the prescribed textbook of Mathematics for Class 10 asks students about the Probability of the coin and whether it will be a 50-paise coin or will not be a Rupees 5 coin. There is a piggy bank that consists of a hundred 50-paise coins, fifty Rupees 1 coins, and twenty Rupees 2 coins, and ten Rupees 5 coins. The possibility of it being equally likely is given regarding the falling of one coin from the piggy bank.
Exercise 15.1 Maths Class 10 PDF Question 11
Class 10 Exercise 15.1, question number 11 includes a question-related about the probability of a male fish beingtaken out of the tank. There is a person named Gopi who buys fish from a shop for his aquarium. The tank contains 13 fishes of which, 5 were male fishes and 8 were female fishes. To make it easy for students, there is a figure to elaborate on the question more clearly.
Exercise 15.1 Class 10 NCERT Solutions Question 12
In question 12 in Exercise 15.1 of Class 10, students are asked about the probability of the arrow that will point towards 8, at an odd number, at a number greater than 2, or at a number less than 9. Probability can be any, but students have to find the best option suitable for the question, and this can be done by following the guidance in NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1.
Exercise 15.1 Class 10 Maths NCERT Solutions Question 13
A dice is thrown once as per the description of Question number 13 of Exercise 15.1, and students have to find the probability of getting a prime number, a number lying between 2 and 6, or an odd number. Students are given three options to find the perfect probability for the question.
Maths Class 10 Chapter 15 Exercise 15.1 Question 14
Question 14 asks about the probability of getting a king of the red colour card, a face card, a red face card, the jack of hearts, a spade, or the queen of diamonds after one card is chosen from the deck of 52 cards.
Chapter 15 Maths Class 10 Exercise 15.1 Question 15
Question 15 of Exercise 15.1 says that there are in total five cards the ten, jack, queen, king and ace of diamonds. All these cards are well-shuffled and facing downward.. Students have to figure out whether the probability of picking up the card is the queen. They are also required to find out what is the possibility that the second card taken is a queen or an ace if the queen is pulled out in the first place and set aside.
Class 10 Maths Chapter 15 Exercise 15.1 Solutions Question 16
According to the aforementioned question, there are 132 good pens but mistakenly, 12 defective pens are mixed in with them. One pen is taken out randomly after the mistake. Now the students have to find out if the probability of the pen which was taken out is a good one.
Ex 15.1 Class 10 Question 17
The first part of Question 17 asks students that there are 20 bulbs in total, of which 4 are defective.. The probability of a defective bulb is being questioned, considering the instance where a random bulb is picked from the lot. The second part of Question 17 says that if the bulb which was chosen earlier is neither defective nor was it was replaced then now what would be the probability of not getting a defective bulb after picking the second bulb from the lot.
Exercise 15.1 Class 10 Question 18
According to the question, there is a box that has 90 discs that are numbered. The probability of taking out a disc which has the depiction of a two-digit number, a perfect square number, or a number divisible by 5 is asked of students in Question 18 of Exercise 15.1.
15.1 Class 10 Question 19
According to Question number 19 of Exercise 15.1, a child has a dice whose six faces are A, B, C, D, E, and A. The question asks about the probability of getting an A or D after the dice is thrown once.
Ex 15.1 Class 10 NCERT Maths Question 20
There is a figure given in the NCERT textbook as an illustration of Question 20 of Exercise 15.1. This question asks students about the probability of dropping the dice in a random area of a rectangular region that has a circle in the middle of it with a diameter of 1m.
15.1 Class 10 Question 21
In Question 21, it says that there is a lot that has 144 ball pens of which 20 are defective. A person named Nuri wants to only buy a good pen. So students have to find the probability of Nuri being able to buy a good pen.
Exercise 15.1 Class 10 Question 22
Question number 22 is related to example 13 of the chapter on Probability in the academic curriculum of Class 10.Students must refer to the example and solve the question. Ex 15.1 Class 10 Question 23
The probability of Hanif losing the game of tossing the coins is what Question 23 asks students. There is a game of tossing a one rupee coin 3 times and discovering the results. It is a given that Hanif will win if the possibility remains the same as 3 heads or 3 tails.
15.1 Class 10 Question 24
A dice is thrown twice according to the narrative in Question 24 of Exercise 15.1 wherein students have to find the probability of whether 5 will not come up either time or 5 will come up at least once.
Ex 15.1 Class 10 Question 25
As the last question of Exercise 15.1, Question 25 requires students to determine whether the given two arguments are correct or not, and along with that, students must explain their answers.
Key Takeaways of NCERT Solutions
NCERT solutions are often seen as one of the most important resources for students preparing for examinations. They cover all the topics taught in the CBSE curriculum and include detailed explanations and examples. The solutions, for example, NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 are written by subject-matter specialists and updated regularly to reflect the latest syllabus changes. NCERT solutions are an essential resource for students. They help students understand the concepts taught in the classroom and prepare for their examinations.
There are a number of key benefits to using NCERT solutions when studying for examinations. Some of these include getting access to high-quality content that has been specifically designed to help students succeed. Getting step-by-step solutions to problems, and having access to revision notes and other resources can help students prepare for exams. In addition, using NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 can help students improve their problem-solving skills. Students can also learn how to approach various types of questions, and develop a deeper understanding of the concepts covered in their course. So, if students want to boost their grades then NCERT solutions like NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 are the best option.
Q.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_____.
Ans
(i) Probability of an event E + Probability of the event ‘not E’ =1.
(ii) The probability of an event that cannot happen is 0. Such an event is called impossible event.
(iii) The probability of an event that is certain to happen is 1. Such an event is called certain event.
(iv) The sum of the probabilities of all the elementary events of an experiment is 1.
(v) The probability of an event is greater than or equal to 0 and less than or equal to 1.
Q.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.
Ans
(i) It does not have equally likely outcomes. The car may never start for some fault.
(ii) It does not have equally likely outcomes as player may take more attempts to shoot a basketball.
(iii) It has equally likely outcomes. The answer of a true-false question is either right or wrong.
(iv) It has equally likely outcomes. The baby is either a boy or a girl.
Q.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?
Ans The outcomes of a coin toss are equally likely. So, the result of a coin toss is completely unpredictable.
Q.4 Which of the following cannot be the probability of an event?
(A) 2/3
(B) –1.5
(C) 15%
(D) 0.7
Ans The correct answer is (B).
Q.5 If P(E) = 0.05, what is the probability of ‘not E’?
Ans Probability of ‘not E’ = 1 – P(E) = 1 – 0.05 = 0.95
Q.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?
Ans
(i) There is no orange flavoured candy in the bag. So, the probability of taking out an orange flavoured candy is zero.
(ii) The probability of taking out lemon flavoured candy is 1 as there are only lemon flavoured candies in the bag.
Q.7 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?
Ans
The probability of 2 students not having the same birthday = P(E’) = 0.992
The probability of 2 students having the same birthday= 1 – P(E’) = 1 – 0.992 = 0.008
Q.8 A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red? (ii) not red?
Ans
Q.9 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?
Ans
Q.10 A piggy bank contains hundred 50p coins, fifty ₹ 1 coins, twenty ₹ 2 coins and ten ₹ 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 50 p coin? (ii) will not be a ₹ 5 coin?
Ans
Q.11 Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see the following figure). What is the probability that the fish taken out is a male fish?
Ans
Q.12 A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see the following figure), and these are equally likely outcomes. What is the probability that it will point at
(i) 8 ?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?
Ans
Q.13 A die is thrown once. Find the probability of getting (i) a prime number; (ii) a number lying between 2 and 6; (iii) an odd number.
Ans
Q.14 One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) a red face card
(iv) the jack of hearts
(v) a spade
(vi) the queen of diamond
Ans
Q.15 Five cards — the ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is the queen?
(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?
Ans
Q.16 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.
Ans
Q.17 (i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
Ans
Q.18 A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.
Ans
Q.19 A child has a die whose six faces show the letters as given below:
A | B | C | D | E | F |
The die is thrown once. What is the probability of getting (i) A? (ii) D?
Ans
Q.20 Suppose you drop a die at random on the rectangular region shown in the following figure. What is the probability that it will land inside the circle with diameter 1m?
Ans
Q.21 A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it?
(ii) She will not buy it?
Ans
Q.22 Two dice, one blue and one grey, are thrown at the same time.
(i) Complete the following table:
Event: ‘Sum of two dice’ |
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Probability |
(ii) A student argues that there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability 1/11. Do you agree with this argument? Justify your answer.
Ans
(i) Total possible outcomes = 36
Possible outcomes for getting the sum 3 are (1, 2) and (2, 1).
Possible outcomes for getting the sum 4 are (1, 3); (3, 1) and (2, 2).
Possible outcomes for getting the sum 5 are (1, 4); (2, 3) (3, 2) and (4,1).
Possible outcomes for getting the sum 6 are (1, 5); (2, 4); (3, 3) (4, 2) and (5, 1).
Possible outcomes for getting the sum 7 are ((1, 6); (2, 5); (3, 4) (4, 3); (5, 2) and (6, 1).
Possible outcomes for getting the sum 9 are (3, 6); (4, 5) ; (5, 4) and (6, 3).
Possible outcomes for getting the sum 10 are (4, 6); (5, 5) and (6, 4).
Possible outcomes for getting the sum 11 are (5, 6) and (6, 5).
Now the complete table is as follows:
Event: ‘Sum of two dice’ |
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Probability |
(ii) No. The eleven sums are not equally likely.
Q.23 A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Ans
Q.24 A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]
Ans
Q.25 Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes — two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is 1/3.
(ii) If a die is thrown, there are two possible outcomes — an odd number or an even number. Therefore, the probability of getting an odd number is 1/2.
Ans
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FAQs (Frequently Asked Questions)
1. Are the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 also available in other languages like Hindi or English?
Yes, Extramarks provide students with both Hindi and English language versions of the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1. Moreover, the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1, can be attained by students on the Extramarks website and Learning App. The website of Extramarks offers students the option to download the NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 in PDF format for later use. The NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 adhere to the format of solutions provided in the prescribed NCERT textbooks to ensure fluidity in learning. Students may get a complete, accurate, and in-depth understanding of the concepts and ideas offered in Chapter 15 on Probability by using NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 in the Hindi language. Besides that, the English version of NCERT Solutions For Class 10 Maths Chapter 15 Exercise 15.1 is also remarkably concise and trustworthy.
2. How can a student ensure that they have prepared effectively for the Mathematics examination, in order to correctly solve the Probability questions in Exercise 15.1 Class 10 without making any mistakes?
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