NCERT Solutions for Class 10 Maths Exercise 14.1 Probability

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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.