11th Maths Samacheer Solutions for chapter 12 எல்லாம் இங்கு உங்களுக்காக தருகின்றோம். Samacheer students க்கு எந்தமாதிரி சொல்லிக்கொடுத்தால் புரியு ஒரு புது முறையை உங்களுக்காக வழங்குகின்றோம்.

11th Maths Samacheer students க்கு எளிதில் புரியும் வகையில் தெளிவாக்குகின்றோம்.

உங்களுக்கு இந்த 11th Maths Samacheer Solution புடித்திருந்தால் நீங்கள் உங்கள் நண்பர்களுக்கு இங்கு share செய்யலாம்.

The initial concept of Probability was formed in the 16th century by two mathematicians from France - Pascal, and Fermat. They both have the credit for creating the fundamentals of Probability. Later the concept was further extended by another mathematician Laplace, who in the 18th century had created the Bayesian concept.

Many of the events in the real world can not be predicted. Hence, we try to take an intelligent guess by defining the probability of the event occurring. We could see extensive use of probability in Games, Calculating charges for a service, Calculating events of default by borrowers.

It is beneficial for students to understand the concepts of Probability as it will be applied in their career in the future when they work for corporate or government agencies. In those organizations, the probability will be used for making business decisions. Instead of making decisions based on experience or chance, it is always appropriate to make decisions based on the mathematical formula using probability.

The events that happen in the world around us are filled with surprises and unpredictable outcomes. So, for an event, there could be multiple types of outcomes that could come. If in reality if we are unable to prepare for more than one outcome, we can at the best prepare for the outcome that is more likely to occur. The probability helps in determining the most likely outcome.

There are five definitions of theory of probability

If the result of the process is already known and can be defined then it is called an Experiment.

If one can in advance predict the outcome of an experiment in a normal condition then the experiment is called a Deterministic Experiment

Another name for Random Experiment is also called as Non-Deterministic Experiment

we know all the possible outcomes of a random experiment But we can predict which of that outcomes will occur

When there are multiple outcomes that are possible in a random event, then each of those single outcomes is called as a simple event

When there are multiple outcomes that are possible in a random event, then the collection of all the possible outcomes is called sample space.

The sample points in a sample space can be of two types: a Countable number of sample points and an Uncountable number of sample points. The uncountable number of sample points cant be further divided into a subcategory. But the countable number of sample points can be classified as either a finite number of sample points or an infinite number of sample points.

In Probability, we need to know about the following things, we first need to know the definition of probability. The probability of any event is favourably divided by possible outcomes. Sample space is denoted by S. Number of elements in sample space is nothing but the possible outcome. When a coin is tossed the sample space is Head, Tail. The number of elements in the sample space is 2. When two coins are tossed at the same time, the sample space is HH, HT, TH and TT. So the number of elements in this sample space is 4. When 3 coins are tossed at the same time then the sample space is HHH, HHT, HTH, HTT, TTH, TTT, THH, THT. The number of elements in the sample space is 8.

Two coins are tossed is the same as one coin tossed two times. Hence we shouldn't get confused with these statements. When 3 coins are tossed, it can also be called one coin tossed three times.

Now we can see the sample space according to Dies. When a die is thrown the sample space is 1,2,3,4,5,6. The number of sample space is 6. When two dies are thrown then the sample space is 11,12,13,14,15, 16,21,22, 23,24,25,26,31,32,33, 34,35,36,41, 42,43,44,45,46,51,52, 53,54,55,56,61,62,63,64,65,66. So the number of elements in the sample space is 6.

The formula to find the number of sample spaces in coins is 2^n. If we put n=1, then the sample space size is 2. If we put the n as 2, then the sample space size is 4. If we put the n as 3, then the sample space size is 8 If we put the n as 4, then the sample space size is 16.

The formula to find the number of sample spaces in dies is 6^n. If we put n=2, then the sample space size is 6. If we put the n as 2, then the sample space size is 36. If we put the n as 3, then the sample space size is 216.