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# Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

## Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

CBSE Class 11 Commerce Maths Statistics And Probability : The CBSE envisions a robust, vibrant and holistic school education that will engender excellence in every sphere of human endeavor. The Board is committed to provide quality education to promote intellectual, social and cultural vivacity among its learners. It works towards evolving a learning process and environment, which empowers the future citizens to become global leaders in the emerging knowledge society. The Board advocates Continuous and Comprehensive Evaluation with an emphasis on holistic development of learners. The Board commits itself to providing a stress-free learning environment that will develop competent, confident and enterprising citizens who will promote harmony and peace.

### Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

CBSE Class 11 Commerce Maths Statistics And Probability : mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between pure mathematics and applied mathematics. However pure mathematics topics often turn out to have applications, e.g. number theory in cryptography. This remarkable fact, that even the “purest” mathematics often turns out to have practical applications, is what Eugene Wigner has called “the unreasonable effectiveness of mathematics”. As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including statistics, operations research, and computer science. Here CBSE Class 11 Commerce Maths Statistics And Probability topics are given :

1. Statistics

Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

2. Probability

Random experiments; outcomes, sample spaces (set representation). Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

### Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

CBSE Class 11 Commerce Maths Statistics And Probability : The Syllabus in the subject of Mathematics has undergone changes from time to time in
accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like engineering, physical and Bioscience, commerce or computer applications.
The present revised syllabus has been designed in accordance with National Curriculum Frame work 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.

### Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

CBSE Class 11 Commerce Maths Statistics And Probability : Addition rules are important in probability.  These rules provide us with a way to calculate the probability of the event “A or B“, provided that we know the probability of A and the probability of B. Sometimes the “or” is replaced by U, the symbol from set theory that denotes the union of two sets. The precise addition rule to use is dependent upon whether event A and event B are mutually exclusive or not.

#### ADDITION RULE FOR MUTUALLY EXCLUSIVE EVENTS

If events A and B are mutually exclusive, then the probability of A or B is the sum of the probability of A and the probability of B.  We write this compactly as follows:

P(A or B) = P(A) + P(B)

#### GENERALIZED ADDITION RULE FOR ANY TWO EVENTS

The above formula can be generalized for situations where events may not necessarily be mutually exclusive. For any two events A and B, the probability of A or B is the sum of the probability of A and the probability of B minus the shared probability of both A and B:

P(A or B) = P(A) + P(B) – P(A and B)

Sometimes the word “and” is replaced by ∩, which is the symbol from set theory that denotes the intersection of two sets.

The addition rule for mutually exclusive events is really a special case of the generalized rule. This is because if A and B are mutually exclusive, then the probability of both A and B is zero.

#### EXAMPLE #1

We will see examples of how to use these addition rules.

Suppose that we draw a card from a well shuffled standard deck of cards.  We want to determine the probability that the card drawn is a two or a face card.  The event “a face card is drawn” is mutually exclusive with the event “a two is drawn.”  So we will simply need to add the probabilities of these two events together.

There are a total of 12 face cards, and so the probability of drawing a face card is 12/52.  There are four twos in the deck, and so the probability of drawing a two is 4/52.  This means that the probability of drawing a two or a face card is 12/52 + 4/52 = 16/52.

#### EXAMPLE #2

Now suppose that we draw a card from a well shuffled standard deck of cards.  Now we want to determine the probability of drawing a red card or an ace.  In this case the two events are not mutually exclusive.  The ace of hearts and the ace of diamonds are elements of the set of red cards and the set of aces.

We consider three probabilities and then combine them using the generalized addition rule.

• The probability of drawing a red card is 26/52
• The probability of drawing an ace is 4/52
• The probability of drawing a red card and an ace is 2/52

This means that the probability of drawing a red card or an ace is:

26/52+4/52 – 2/52 = 28/52.

### Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

CBSE Class 11 Commerce Maths Statistics And Probability : Probability and statistics are two closely related mathematical subjects. Both use much of the same terminology and there are many points of contact between the two. It is very common to see no distinction between probability concepts and statistical concepts. Many times material from both of these subjects gets lumped under the heading “probability and statistics,” with no attempt to separate what topics are from which discipline.

Despite these practices and the common ground of the subjects, they are distinct. What is the difference between probability and statistics?

#### WHAT IS KNOWN

The main difference between probability and statistics has to do with knowledge. By this, we refer to what are the known facts when we approach a problem. Inherent in both probability and statistics is a population, consisting of every individual we are interested in studying, and a sample, consisting of the individuals that are selected from the population.

A problem in probability would start with us knowing everything about the composition of a population, and then would ask, “What is the likelihood that a selection, or sample, from the population, has certain characteristics?”

#### EXAMPLE

We can see the difference between probability and statistics by thinking about a drawer of socks. Perhaps we have a drawer with 100 socks. Depending upon our knowledge of the socks, we could have either a statistics problem or a probability problem.

If we know that there are 30 red socks, 20 blue socks, and 50 black socks, then we can use probability to answer questions about the makeup of a random sample of these socks. Questions of this type would be:

• “What is the probability that we draw two blue socks and two red socks from the drawer?”
• “What is the probability that we pull out 3 socks and have a matching pair?”
• ”What is the probability that we draw five socks, with replacement, and they are all black?”

If instead, we have no knowledge about the types of socks in the drawer, then we enter into the realm of statistics. Statistics helps us to infer properties about the population on the basis of a random sample. Questions that are statistical in nature would be:

• A random sampling of ten socks from the drawer produced one blue sock, four red socks, and five black socks. What is the total proportion of black, blue and red socks in the drawer?
• We randomly sample ten socks from the drawer, write down the number of black socks, and then return the socks to the drawer. This process is done five times. The mean number of socks is for each of these trials is 7. What is the true number of black socks in the drawer?

#### COMMONALITY

Of course, probability and statistics do have much in common. This is because statistics is built upon the foundation of probability. Although we typically do not have complete information about a population, we can use theorems and results from probability to arrive at statistical results. These results inform us about the population.

Underlying all of this is the assumption that we are dealing with random processes.

This is why we stressed that the sampling procedure we used with the sock drawer was random. If we do not have a random sample, then we are no longer building upon assumptions that are present in probability.

Probability and statistics are closely linked, but there are differences. If you need to know what methods are appropriate, just ask yourself what it is that you know.

### Complete Details Of CBSE Class 11 Commerce Maths Statistics And Probability

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