Find the best tutors and institutes for Class 10 Tuition
Q13(iii):
A die is thrown once. Find the probability of getting (iii) an odd number.
Solution :
Given: A fair six-faced die is thrown once. The possible outcomes are the integers from 1 to 6.
To Find: The probability of getting an odd number.
Step 1: Defining the Sample Space
Let $S$ be the sample space representing all possible outcomes when a die is thrown. Since a standard die has six faces numbered 1 through 6:
$S = \{1, 2, 3, 4, 5, 6\}$
The total number of possible outcomes, denoted by $n(S)$, is:
$n(S) = 6$
Step 2: Defining the Event
Let $E$ be the event of getting an odd number. An odd number is an integer that is not divisible by 2. From the sample space $S$, we identify the odd numbers:
$E = \{1, 3, 5\}$
The number of favorable outcomes, denoted by $n(E)$, is:
$n(E) = 3$
Step 3: Applying the Probability Formula
The probability of an event $P(E)$ is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in the sample space:
$P(E) = \frac{n(E)}{n(S)}$
[Using the classical definition of probability for equally likely outcomes]
Step 4: Calculation
Substitute the values obtained in Step 1 and Step 2 into the formula:
$P(E) = \frac{3}{6}$
To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor, which is 3:
$P(E) = \frac{3 \div 3}{6 \div 3} = \frac{1}{2}$
Final Answer: The probability of getting an odd number is $\frac{1}{2}$ (or 0.5).
More Questions from Class 10 Mathematics Probability EXERCISE 14.1
- Q1(i): Complete the following statements: (i) Probability of an event $E$ + Probability of the event ‘not $E$’ = .
- Q1(ii): Complete the following statements: (ii) The probability of an event that cannot happen is . Such an event is called .
- Q1(iii): Complete the following statements: (iii) The probability of an event that is certain to happen is . Such an event is called .
- Q1(iv): Complete the following statements: (iv) The sum of the probabilities of all the elementary events of an experiment is .
- Q1(v): Complete the following statements: (v) The probability of an event is greater than or equal to and less than or equal to .
- Q10(i): 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 ?
- Q10(ii): 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 (ii) will not be a ` 5 coin?
- Q11: 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 Fig. 14.4). What is the probability that the fish taken out is a male fish?
- Q12(i): 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 Fig. 14.5 ), and these are equally likely outcomes. What is the probability that it will point at (i) 8 ?
- Q12(ii): 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 Fig. 14.5 ), and these are equally likely outcomes. What is the probability that it will point at (ii) an odd number?
- Q12(iii): 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 Fig. 14.5 ), and these are equally likely outcomes. What is the probability that it will point at (iii) a number greater than 2?
- Q12(iv): 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 Fig. 14.5 ), and these are equally likely outcomes. What is the probability that it will point at (iv) a number less than 9?
- Q13(i): A die is thrown once. Find the probability of getting (i) a prime number;
- Q13(ii): A die is thrown once. Find the probability of getting (ii) a number lying between 2 and 6;
- Q14(i): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour
- Q14(ii): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (ii) a face card
- Q14(iii): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (iii) a red face card
- Q14(iv): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (iv) the jack of hearts
- Q14(v): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (v) a spade
- Q14(vi): One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (vi) the queen of diamonds
- Q15(i): 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?
- Q15(ii)(a): 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. (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace?
- Q15(ii)(b): 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. (ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (b) a queen?
- Q16: 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.
- Q17(i): (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?
- Q17(ii): (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 ?
- Q18(i): 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
- Q18(ii): 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 (ii) a perfect square number
- Q18(iii): 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 (iii) a number divisible by 5.
- Q19(i): A child has a die whose six faces show the letters as given below: The die is thrown once. What is the probability of getting (i) A?
- Q19(ii): A child has a die whose six faces show the letters as given below: The die is thrown once. What is the probability of getting (ii) D?
- Q2(i): 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.
- Q2(ii): Which of the following experiments have equally likely outcomes? Explain. (ii) A player attempts to shoot a basketball. She/he shoots or misses the shot.
- Q2(iii): Which of the following experiments have equally likely outcomes? Explain. (iii) A trial is made to answer a true-false question. The answer is right or wrong.
- Q2(iv): Which of the following experiments have equally likely outcomes? Explain. (iv) A baby is born. It is a boy or a girl.
- Q20: Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter $1$m?
- Q21(i): 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 ?
- Q21(ii): 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 (ii) She will not buy it ?
- Q22(i): Refer to Example 13. (i) Complete the following table:
- Q22(ii): Refer to Example 13. (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 $\frac{1}{11}$. Do you agree with this argument? Justify your answer.
- Q23: 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.
- Q24(i): A die is thrown twice. What is the probability that (i) 5 will not come up either time? [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]
- Q24(ii): A die is thrown twice. What is the probability that (ii) 5 will come up at least once? [Hint : Throwing a die twice and throwing two dice simultaneously are treated as the same experiment]
- Q25(i): 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 $\frac{1}{3}$.
- Q25(ii): Which of the following arguments are correct and which are not correct? Give reasons for your answer. (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 $\frac{1}{2}$.
- Q3: 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?
- Q4: Which of the following cannot be the probability of an event?
- Q5: If $P(E) = 0.05$, what is the probability of ‘not $E$’?
- Q6(i): 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?
- Q6(ii): 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 (ii) a lemon flavoured candy?
- Q7: 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?
- Q8(i): 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 ?
- Q8(ii): 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 (ii) not red?
- Q9(i): 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 ?
- Q9(ii): 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 (ii) white ?
- Q9(iii): 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 (iii) not green?
CBSE Solutions for Class 10 Mathematics Probability
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Probability
Super Tutor
BTM 6th Stage, Bangalore
11 yrs of
Exp
11 students
829 hrs of classes completed
600
per hour
Online Classes
Student's Home
With over 11 years of teaching experience, I have had the privilege of mentoring more than 5,000 students across various reputed coaching institutes in Bangalore. My teaching has primarily focused on preparing students for competitive exams, and I take pride in the fact that many of my students have successfully qualified for NEET, JEE and CET under my guidance. Throughout my career, I have been committed to delivering clear, concept-driven instruction while fostering a supportive and open classroom environment. I ensure that every student, regardless of their level, feels comfortable asking questions and engaging actively in the learning process. My ability to simplify complex topics and build strong student rapport continues to be the cornerstone of my teaching approach.
Top Tutor
MSR nagar mathikere, Bangalore
20 yrs of
Exp
21 students
5390 hrs of classes completed
499
per hour
Online Classes
I enjoy teaching and making things easier and fun for the children. Didn't send my kids for any tuitions. Today the elder child is a CSE graduate , working for Amazon & the other is in her 3rd year MBBS !
I have been studying Maths and Science under her guidance since 8th grade. She explains every concept in a simple and clear way, making even difficult topics easy to understand. Her teaching style is patient and supportive, and she always makes sure all doubts are cleared. She focuses on strengthening basics and gives regular practice, which has really helped me improve. Because of her guidance, my confidence in both subjects has increased a lot. I am truly grateful for her dedication and support
Top Tutor
Kurichimuttom, Kozhencherry
7 yrs of
Exp
4 students
379 hrs of classes completed
350
per hour
Online Classes
I have taught almost 50 students.
The best teacher my daughter have ever got. She can understand everything that she took and also did many question papers. She could write everything that her teacher teaches her and the teacher is very lovely.
Top Tutor
Gharoli Gharoli, Delhi
16 yrs of
Exp
1 student
23 hrs of classes completed
2000
per hour
Online Classes
I bring with me 17 years of diverse experience in the pharmaceutical industry along with academic expertise, combining strong practical knowledge with a passion for teaching. I am dedicated to simplifying complex concepts and delivering them in an engaging manner, ensuring that students not only gain subject knowledge but also develop the skills, confidence, and potential required to achieve academic excellence and become industry-ready professionals.
I highly recommend this teacher to anyone looking for a clear and effective learning experience. The teaching style is simple, engaging, and easy to follow, which makes even difficult topics understandable. Every chapter is explained in depth, with attention to important concepts and details, ensuring that students build a strong foundation. The teacher is patient, knowledgeable, and dedicated to helping students succeed. Lessons are well-structured, and examples are used effectively to make learning more practical and enjoyable. This approach boosts confidence, improves understanding, and encourages active participation. Overall, an excellent teacher who makes learning both meaningful and enjoyable.
Top Tutor
Ashok Vihar, Delhi
10 yrs of
Exp
2 students
121 hrs of classes completed
380
per hour
Online Classes
Student's Home
Being a professional tutor , I have an experience of more than 9 years , my students are my strength , i always dedicated for my students.
A+ tutor for Maths and Science class 10. Highly recommended, very humble and polite. You should go for him without doubts.
Find more Tutor for Probability in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
