Author name: Narender Kumar

Probability is one of the important chapters of Class 10 Maths for the CBSE Board Exam 2026-27. Practising Class 10 Maths Probability Previous Years Questions helps students understand outcomes, events, favourable outcomes and the calculation of probability. Previous years’ questions also help students become familiar with different question patterns and improve their confidence and accuracy for the CBSE Board Exam 2026-27. For effective exam preparation, students should practise Class 10 Maths Most Important Probability Previous Years Questions along with NCERT questions, important questions and sample papers. Previous years’ questions help students understand the type, level and pattern of questions that can be asked in the CBSE Board Exam. In this post, you will find important Probability questions for Class 10 Maths. Video solutions are also available, so students can first try to solve each question themselves and then watch the video solution to understand the correct method. What is Probability? Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. In simple words, probability tells us how likely or unlikely an event is to happen. For example: The probability of an event is calculated using: Probability of an event = Number of favourable outcomes / Total number of possible outcomes If E is an event, then: P(E) = Number of favourable outcomes / Total number of outcomes The value of probability always lies between 0 and 1. Why is Probability Important for Class 10 CBSE Board Exams? Probability is an important part of the Class 10 CBSE Maths syllabus and students should not ignore it while preparing for their board examinations. Practising Class 10 Maths Probability Previous Years Questions can help students in several ways. 1. Understand the Question Pattern Previous years’ questions give students an idea of how probability questions are framed in the CBSE examination. Questions may involve: 2. Improve Problem-Solving Skills Probability questions require students to identify: Regular practice helps students solve these questions more confidently. 3. Prepare for Different Types of Questions CBSE examination questions can test the same concept in different ways. Practising previous years’ questions helps students become familiar with different formats. 4. Improve Accuracy Probability questions are often based on counting outcomes correctly. A small mistake in identifying the total or favourable outcomes can lead to an incorrect answer. Practising previous years’ questions helps students improve accuracy. 5. Useful for Revision Probability is a comparatively compact chapter. Once students understand the basic concepts and practise important questions, they can revise the chapter effectively before the CBSE Board Exam 2026-27. Class 10 Maths Most Important Probability Previous Years Questions Q1.A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen. Q2.A box contains cards numbered 6 to 50. A card is drawn at random from the box. Calculate the probability that the drawn card has a number which is a perfect square. Q3.A number is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3. What will be the probability that square of this number is less than or equal to 1? Q4.If two different dice are rolled together, calculate the probability of getting an even number on both dice. Q5.A coin is tossed two times. Find the probability of getting both heads or both tails. Q6.In a simultaneous toss of two coins, find the probability of getting:(i) exactly one head,(ii) atmost one head. Q7. Three coins are tossed simultaneously. Find the probability of getting exactly two heads. Q8.A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king. Q9.The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 14 . The probability of selecting a blue ball at random from the same jar is 13 . If the jar contains 10 orange balls, find the total number of balls in the jar. Q10.A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16. Watch the Solutions Below are some important types of Probability questions that Class 10 students should practise. Question 1: Coin Toss A coin is tossed once. Find the probability of getting: (i) a Head(ii) a Tail. Question 2: Throwing a Die A die is thrown once. Find the probability of getting: (i) an even number(ii) a prime number(iii) a number greater than 4. Question 3: Playing Cards A card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability of getting: (i) a king(ii) a red card(iii) an ace(iv) a face card. Question 4: Numbers A number is selected at random from a set of numbers. Find the probability that the selected number satisfies the given condition. Such questions test the student’s ability to identify the total outcomes and favourable outcomes. Question 5: Real-Life Selection A student or object is selected randomly from a given group. Find the probability of selecting an object or person satisfying a particular condition. These questions are useful because they connect probability with everyday situations. Tip: Before solving any probability question, clearly write the total number of possible outcomes and the number of favourable outcomes. Why Should You Practise Previous Years Questions? Previous Years Questions (PYQs) are extremely useful for examination preparation because they provide practice with questions that have appeared in earlier examinations. When preparing for the CBSE Board Exam 2026-27, students should follow a systematic approach: This approach can help students develop both conceptual understanding and exam-solving speed. Watch Video Solutions of Probability Questions Reading a solution is useful, but watching a step-by-step explanation can make difficult questions easier to understand. For the important Probability questions covered in this post, video solutions

To understand Understanding Potential Difference in an Electric Field, we should first develop a clear idea of potential energy. A simple gravitational example helps us build this connection. Just as an object possesses gravitational potential energy because of its position in a gravitational field, a charged particle can possess electric potential energy because of its position in an electric field. This analogy provides a strong foundation for understanding electric potential, potential difference, voltage, and electric potential energy. Once these ideas are connected logically, many concepts in electricity become much easier to understand. The aim is not merely to memorize formulas, but to develop a physical understanding that helps science students clear their doubts and confidently move towards more advanced concepts of electricity and electric fields. Gravitational Potential Energy: A Simple Analogy Suppose an object of mass mm is lifted from point A on the ground to point B, at a height hh. The gravitational force acting on the object is F=mg where: If the object is lifted through a vertical distance hh, the work done against gravity is W=F×d Therefore,W=mg×hW=mg\times h orW=mghW=mgh This work does not simply disappear. It is stored as gravitational potential energy of the object. Therefore, at height hh, U=mgh​ where UU represents gravitational potential energy. For convenience, we can choose the ground as the reference level and take the gravitational potential energy there to be zero. Thus, UA​=0 and at point BB,UB=mghU_B=mgh But what is gravitational potential? Here we need to make an important distinction. Potential energy depends on the mass of the object: U=mgh whereas gravitational potential is potential energy per unit mass:ϕ=Um=gh\phi=\frac{U}{m}=gh So, gravitational potential tells us about the potential energy available per unit mass at a particular point in a gravitational field. This idea helps us understand electric potential. What Is Electric Potential? An electric field is a region of space in which an electric charge experiences an electric force. To define the electric potential at a point, we consider a small positive test charge and calculate the work required to bring it from a reference point to that location. Usually, for an isolated charge system, infinity is taken as the reference point and the electric potential at infinity is taken to be zero. Therefore, the electric potential at a point is defined as: The work done by an external agent in bringing a unit positive test charge from infinity to that point, without changing its kinetic energy. Mathematically, V=W​​/Q where: The SI unit of electric potential is the volt (V). One volt is defined as: 1 V=1 J/C​ This means that if 1 joule of work is required to bring a 1 coulomb positive charge to a point, the electric potential of that point is 1 volt relative to the chosen reference. Electric Potential and Electric Potential Energy Are Different This distinction is very important. Electric potential VV is potential energy per unit charge: V=U​​/Q Therefore, U=V​Q Here: This is analogous to gravitational potential: Gravitational potential = Gravitational potential energy Mass Similarly, Electric potential = Electric potential energy Charge So, just as gravitational potential tells us about energy per unit mass, electric potential tells us about energy per unit charge. What Is Potential Difference? Now consider two points, A and B, in an electric field. Suppose their electric potentials are VAV_A and VBV_B. The potential difference between A and B is the difference between their electric potentials: VAV_A – VBV_B If a charge Q moves from A to B, the change in its electric potential energy is related to the potential difference. For a positive charge, the work done by the electric field in moving the charge from A to B is W=Q( VAV_A – VBV_B )​ Therefore, VAV_A – VBV_B ​=W​​/Q where WW here represents the work done by the electric field. There is an important point here: if we instead talk about the work done by an external agent in moving the charge slowly from A to B, the sign is reversed: Wexternal​=Q(VB​−VA​) This distinction prevents confusion about the sign of work. Why Does Potential Difference Produce Electric Current? A potential difference does not automatically mean that current will flow. For current to flow continuously, there must generally be a closed conducting path and mobile charge carriers. When a potential difference is applied across a conductor, an electric field is established inside the conductor. This electric field exerts force on the mobile charge carriers and causes their net drift motion. This organized movement of charge is called electric current. Therefore, we can say: Potential difference provides the energy per unit charge that drives charge through a circuit. When a conducting path is available, this can produce an electric current. For example, a battery maintains a potential difference between its terminals. When the terminals are connected through a conducting circuit, charges move through the circuit and current flows. Potential Difference Across a Conductor Suppose a conductor is connected between points A and B. If the potential at A is VAV_A and the potential at B is VBV_B, then the potential difference is V=VAV_A​−VBV_B if we define the voltage from A to B in that direction. If a charge QQ moves through a potential difference VV, the corresponding energy transferred is W=QV​ Therefore, V= W/Q This equation gives the physical meaning of voltage: Voltage tells us how much energy is transferred per unit charge. For example, a potential difference of 12 V means that 12 joules of energy are transferred per coulomb of charge. 12 V=12 J/C How Is a Potential Difference Generated Between Clouds and the Earth? One of the most spectacular examples of a very large potential difference in nature is lightning. Inside a thundercloud, powerful upward and downward air currents cause collisions among ice crystals, supercooled water droplets, and larger ice particles such as graupel. These collisions can cause charge separation within the cloud. As a result, different regions of the cloud acquire different net charges. Typically, the lower part of a thundercloud becomes predominantly negatively charged, while the upper region becomes