In our day-to-day life, we make so many predictions like, is it going to rain tomorrow or not? will India win the next match or not? we even make predictions about something as vague as what will happen to the planet after 100 or 1000 years. We know that predictions are based on probabilities, and in-class 10 maths chapter 15 probability, we will learn these probabilities can be measured numerically.
The origin of probability is said to be from gambling, but as time progressed, it became an integral part of maths and is now being used in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc.
Class 10 Maths Chapter 15 Probability
We were introduced to probability in the previous classes, and we learned a few things about this topic there. Of course, we will add to that knowledge in this class, but first, we must make sure that we remember what we had learned in the earlier class. So, here are the important points:
Trial: A trial is an action that results in one or more than one outcome, and the outcome is simply the result of an action. e.g if you roll a dice once then it is your trial 1 and there can be 6 outcomes as a dice has 6 faces.
Experimental or empirical probabilities: The probabilities that are based on the results of an actual experiment are called experimental or empirical probabilities. e.g Suppose we take 100 trials of tossing a coin and note down the outcomes of every trial. After completing the 100th trial we found that 51 times the outcome was heads and 49 times tail.
So, the empirical probability of heads will be 51/100. Note that this is just for the 100 trials that we did, if we continue with our trials then they will be different, this is why it is called experimental probabilities.
These were the terms that we saw in class 9th NCERT book, in-class 10 maths chapter 15 probability we will learn a lot, but first, let’s take a look at the summary of the previous class.
- An event for an experiment is the collection of some outcomes of the experiment.
- The empirical (or experimental) probability P(E) of an event E is given by
P(E) = Number of trials in which E has happened / Total number of trials - The Probability of an event lies between 0 and 1.
Class 10 Maths Chapter 15 Probability
Now let’s get familiar with the important terms that we will use in class 10 maths chapter 15 probability so that there is no doubt when you go on to practice the problems from this chapter.
Equally likely outcomes: When the probability of one outcome is the same as that of the other outcome, then the outcome is known as equally likely. e.g if we toss a coin then the outcomes of heads and teal are equally likely.
In simple words, when every outcome has equal chances of occurring, then the outcomes can be said as equally likely. But, not every event will have equally likely outcomes. e.g suppose there are 4 red balls and 2 green balls in a bag (the size and shape of all the balls are the same), and you are to draw a ball out of that bag without looking inside.
In this case, the probability of drawing a green ball is not equally likely, because green balls are not same as the red balls.
Theoretical probability: Unlike empirical probability, the theoretical probability is based on reasoning and logic. We do not actually conduct any experiment, instead, we just make predictions based on certain logic and reasoning.
e.g If we were to determine the probability of coming head if a coin is tossed 10 million times, then we would simply say 1/2 because tossing the coin 10 million times is time-consuming and almost impossible to do.
In fact, in class 10 maths chapter 15 probability, we will practice a lot of problems based on theoretical probability. It is also known as classical probability and is given by the formula
P(E) = a number of outcomes favorable to E / Number of all possible outcomes of the experiment, here we assume that the outcomes of the experiment will be equally likely.
Class 10 Maths Chapter 15 Probability
Though probability is a never-ending branch of mathematics, but, as we have seen in earlier classes, CBSE keeps it short by giving only 1 or 2 exercises in the NCERt book. Also, there is barely 1 topic to cover in each class, but, long or short, we have to study it anyway.
Elementary event: The event that has only one outcome in an experiment is called the elementary event. e.g while tossing a coin the outcome will either be heads or tail. This concludes that the sum of the probabilities of all the elementary events of an experiment will always be 1.
Complementary events: Two events are said to be complementary when one event occurs if and only if the other does not. e.g when a coin is tossed, heads will come only if tails don’t. In other words, one of the complementary events can occur at a time.
Impossible events: Those events which are impossible to occur in an experiment are called impossible events. e.g the probability of coming any number more than 6 while rolling dice is 0 or impossible because a dice only has 6 faces and hence only numbers up to 6. The probability of impossible events is always 0.
Sure or certain events: These are the events that are certain or sure to occur in an experiment. e.g while rolling dice, it’s certain that a number less than 6 will occur because a dice has all numbers less than 7. The probability of such events is always 1.
So these are all the terms and topics that you will learn in class 10 maths chapter 15 probability. Now let’s take a look at the blueprint of this chapter.
| class 10 maths chapter 15 probability blueprint | |
|---|---|
| 1 Marker | 2 question |
| 3 Marker | 1 question |
| Total questions | 3 |
| Total marks | 5 |
Clearly, as the table shows, there will be 2 questions of 1 mark and 1 question of 3 marks in the board exam from this chapter. Total 3 questions of 5 marks will come from probability, therefore, prepare it wisely as it is an easy chapter, and one can score good marks in it.
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