NCERT Solutions for Class 10 Maths Exercise 14.1 Probability

To prepare for the exercise in Chapter 14 of Class 10 Maths on Probability, it is important to first have a thorough understanding of the basic concepts such as theoretical probability, equally likely outcomes, and complementary events. Start by practicing each example provided in the chapter, as they form the foundation of understanding how probability calculations work in different scenarios. Focus on solving questions related to tossing coins, rolling dice and drawing cards, as these are common examples that appear frequently in exams. Understanding these basic problems will help build the skills needed to tackle more complex probability questions.

Next, work on solving the exercise thoroughly. Make sure to answer all the questions, paying special attention to those involving real-life scenarios like drawing balls from a bag or selecting cards from a deck. These questions often test your ability to apply probability concepts in practical situations. Practice using formulas like 𝑃(𝐸) = (favorable outcomes)/(total outcomes) and remember that the sum of probabilities for all possible outcomes is always 1. By consistently practicing these problems, you will be well-prepared for the exam and more confident in solving probability questions accurately.

All the question answers of NCERT Books are solved for CBSE, UP Board, MP Board and all other boards who are using NCERT Textbooks for academic session 2024-25. Contents are based on latest CBSE Syllabus 2024-25 and updated for Exams. Download here, Standard 10 Maths Exercise 14.1 in Hindi and English Medium free of cost. Videos related to each questions are also given here to make study easier and simple.

Probabilities are based on the results of an actual experiment, then they are called experimental or empirical probabilities. In fact, experimental probabilities are based on the results of a proper record of actual experiments and the occurrence of events. Furthermore, these possibilities are only “estimates”. If we run the same experiment 1000 times, we can get different data which gives different possibilities.

How to find Probability?

Suppose if an experiment is a million times or more that this? And similarly, what would be the experimental probability of a head?” The number of throws, the experimental probability number of a tail or a head is near about to be set to 0.5, which we generally call the theoretical probability of obtaining a head or tail., As you will do in the next section. In Chapter 15 of Standard Mathematics 10, we introduced the theoretical probability of an event (also called classical) and discussed simple problems based on this concept.

Equally Likely Events

Suppose another example of equally likely outcomes, whenever we throw a die once. We always know that a die will always mean a fair die. Can you think, what are the possible outcomes? Yes, it will be 1, 2, 3, 4, 5, 6. Each number has the same possibility to occur. So the equally likely outcomes of throwing a die are 1, 2, 3, 4, 5, and 6.

Probability — A Theoretical Approach

When we talk about a coin, we assume that it is “proper”, that is, it is symmetric, so there is no reason why it should go down more often from one side than the other. We call this property of coin “fair”. By the phrase “random toss”, we mean that the coin can fall freely without bias or interference. We know that the coin can descend only in two possible ways, either above its head or with its tail (we rule out the possibility that it will “land” on its edge, which might be possible, e.g. For, if it falls on the sand). We can reasonably assume that each result, head or tail, is likely to be the other. We refer to this by saying that head and tail are equally likely to result.

Assumption Based Probability

By repeatedly experimenting where we formulate some assumptions, repeating an experiment can be avoided because the assumptions help directly calculate the exact (theoretical) probability. The notion of equally likely outcomes (which is valid in many experiments, as in the last two examples, one for coin and one for die) is an assumption that leads us to the next definition of probability of an event.