The CBSE envisions a robust, vibrant and holistic school education that will engender excellence in every sphere of human endeavour. 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.
About Academics UnitThe goal of the Academic, Training, Innovation and Research unit of Central Board of Secondary Education is to achieve academic excellence by conceptualising policies and their operational planning to ensure balanced academic activities in the schools affiliated to the Board. The Unit strives to provide Scheme of Studies, curriculum, academic guidelines, textual material, support material, enrichment activities and capacity building programmes. The unit functions according to the broader objectives set in the National Curriculum Framework-2005 and in consonance with various policies and acts passed by the Government of India from time to time.
Some major objectives of the Unit are:
| i. To define appropriate approaches of academic activities to provide stress free, child centred and holistic education to all children without compromising on quality |
ii. To analyse and monitor the quality of academic activities by collecting the feedback from different stakeholders
iii. To develop norms for implementation of various academic activities including quality issues; to control and coordinate the implementation of various academic and training programmes of the Board; to organize academic activities and to supervise other agencies involved in the process
iv. To adapt and innovate methods to achieve academic excellence in conformity with psychological, pedagogical and social principles.
v. To encourage schools to document the progress of students in a teacher and student friendly way
vi. To propose plans to achieve quality benchmarks in school education consistent with the National goals
vii. To organize various capacity building and empowerment programmes to update the professional competency of teachers
G O Y A L B R O T H E R S P R A K A S H A N
Assignments in Mathematics Class X (Term II)
The science which measures the degree of uncertainty is called
There are two types of approaches to the study of probability. These are experimental or empirical approach and theoretical approach.
In the experimental approach to probability, we
nd the probability of the occurrence of an event
by actually performing the experiment a number of
times and record the happening of an event.
In the theoretical approach to probability, we predict the results without actually performing the experiment.
The observations of an experiment are called its
An experiment in which all possible outcomes are known and the exact outcome cannot be predicted
in advance, is called a
means each outcome is equally likely to occur. For example, an unbiased die indicates that each of the outcomes 1, 2, 3, 4, 5 or 6 has equal chances to occur. Throughout this chapter, we shall
assume that all the experiments have equally likely
The theoretical probability of an event E, written as P(E) is dened as
Number of outcomes f
Total number of all possible
ooutcomes of the experiment
IMPORTANT TERMS, DEFINITIONS AND RESULTS
An event having only one outcome of the experiment is called an elementary event.
The sum of the probabilities of all the elementary
events of an experiment is 1.In general for any event EP(E) = 1 – P(not E) = 1 –
= 1 – P(E)or P(E) +
= 1Here the event
representing not E, is called the compliment of the event E.
The probability of the event which is impossible to occur is 0. Such an event is called an
The probability of an event which is sure (or certain) to occur is 1. Such an event is called a
For an event E, we have 0
A die is a well balanced cube with its six faces marked with numbers or dots 1 to 6. When we throw a die we are interested in the number that occurs on the top face.
The pack or deck of playing cards consists of 52 cards, 26 of red colour and 26 of black colour. There are four suits each of 13 cards namely hearts (
), diamonds (
) and clubs (
).Each suit contains ace, king, queen, jack or knave,
10, 9, 8, 7, 6, 5, 4, 3, 2.
There are 4 aces, 4 kings, 4 queens, 4 jacks, 4 tens,
and so on in a pack.
Kings, queens, and jacks are called face cards.
MULTIPLE CHOICE QUESTIONS
A. Important Questions
The theoretical probability P(E) of an event E is dened as : (a)
E(b) P(E) = No. of outcomes favourable to E × No.
of all possible outcomes of the experiment
(d) none of these
Which of the following can be the probability of
an event?(a) – 0.02 (b) 1.4 (c)
Which of the following cannot be the probability
of an event? (a)
(b) 0.2 (c) 4% (d)
Getting a number 8 in a single throw of a die