Direct Recruitment to the Special Class Railway Apprentices' is made through the Union Public Service Commission (UPSC) on the basis of the Annual Competitive Examinations. Recruitment to the Indian Railway Traffic Service (IRTS) and the Indian Railway Accounts Service (IRAS) is done on the basis of the result of the Civil Services Examination (The Indian Administrative service examination) and that to the Indian Railway services of Engineers (IRSE), Indian Railway Service of Electrical Engineers (IRSEE) and Indian Railway Services Stores (IRSS) is made on the basis of the Combined Engineering Service Examination.
Recruitment of Clerks, Assistant Station masters, Ticket Collectors, train Collectors and other vacancies is also done through direct recruitment by the Railway Recruitment Boards in different states. Depending upon the vacancies that arise, these boards call out for exams for different posts. These Boards are located at 19 centres in Allahabad (www.rrbald.nic.in), Ahmedabad, Ajmer( www.rrbajmer.org), Chandigarh, Jammu, Gorakhpur, Patna (www.rrbpatna.org) , Guwahati, Calcutta, Bhubaneswar( www.rrbbbs.org), Chennai (www.rrbchennai.net), Trivandrum, Bangalore, Secunderabad (www.rrbsc.org), Mumbai, Bhopal , Malda, Ranchi etc. The Boards advertise the vacancies through newspapers and the Employment News and conduct both written examinations and interviews. Recruitment is made in the lowest grades to these categories and prescribed qualification is generally matriculation. For some posts like Commercial Apprentice, Traffic Apprentice, Asstt. Station Master, Clerk Grade I, guards etc., prescribed qualification is a degree from a recognised University.
For Recruitment to the Indian Railway Service Mechanical Department, there is a dual method, one is by Combined Engineering Service Examination and the other is UPSC Special Class Railway Apprentices' Examination. Approximately, 50 percent are recruited as the Special Class Railway Apprentices through the U.P.S.C. Exam. This examination is held once a year, generally in the month of July. Blank application forms and other particulars are published in Employment News, generally in the month of February.
A candidate must be either a citizen of India, or a subject of Nepal, or a subject of Bhutan, or a Tibetan refugee who came over to India before 1st January, 1962 with the intention of permanently settling in India. or a person of Indian origin who has migrated from Pakistan, Burma, Sri Lanka, East African countries of Kenya, Uganda, the United Republic of Tanzania, Zambia, Malawi, Zaire, Ethiopia or from Vietnam with the intention of permanently settling in India.
Educational qualification -
Age: Minimum 17 years and maximum age should be less than 21 years as on August 1 of the year of examination. Age is relaxable for SC/ST and certain other categories.
Fee: Rs.50/- is payable by the Candidates seeking admission to the examination .Candidates belonging to SC/ST are not required to pay any fee.
The UPSC have developed an application form common for all their examinations which will be processed on computerized machines. This application form along with an Information Brochure containing general instructions for filling up the form, an acknowledgement card and an envelope for sending the application is obtainable from the designated Head Post Offices/Post Offices throughout the country as listed below of Notice against cash payment of Rs. 20/- (Rupees twenty only). Form should be purchased from the designated Post Offices only and not from any other agency. This form can be used only once and for only one examination. Candidates must use the form supplied with the Information Brochure only and they should in no case use photocopy/reproduction/unauthorized printed copy of the Form. Since this form is electronically scanable, due care should be taken to fill up the application form correctly. The candidates should also fill up in the relevant places of the Acknowledgement Card, their Application Form Number (8-digit) and the name of the examination. The applicants are required to affix the postage stamp of Rs. 6/- on the Acknowledgement Card and send the same along with application form to UPSC. If an applicant fails to affix the postage stamp of requisite amount his acknowledgement card will not be despatched and Commission will not be responsible for non-receipt of acknowledgement card by the applicant. The duly filled in application form and the acknowledgement card should then be mailed in the special envelope supplied with the Information Brochure. You should also write the name of examination viz. "Special Class Railway Apprentices' Examination, (& Year in which examination is held )" on the envelope before despatching it to
"Secretary, Union Public Service Commission, Dholpur House, New Delhi-110069".
List of Head Post Offices/Post Offices where UPSC application forms are available:
Andhra Pradesh Circle : Hyderabad GPO, Hyderabad Jubilee, Kachiguda Stn., Khairatabad, Secunderabad, Trimulgherry, Adilabad, Anantapur, Arundelpet (Guntur), Chittoor, Cuddapah, Eluru, Kakinada, Karimnagar, Khammam, Kurnool, Machilipatnam, Mahboobnagar, Medak, Nalgonda, Nellore, Nizamabad, Ongole, Srikakulam, Vizianagaram, Vijayawada, Vikarabad, Visakhapatnam, Warangal.
Assam Circle : Guwahati, Barpeta, Dhubri, Dibrugarh, Diphu, Golaghat, Hailakandi, Jorhat, Karimganj, Kokrajhar, Mangaldoi, Nagaon, Nalbari, North Lakhimpur, Sibsagar, Silchar, Tezpur, Tinsukia.
Bihar Circle : Patna, GPO, Bankipur, Arrah, Aurangabad, B. Deoghar, Bokaro Steel City, Banka, Battiah, Begusarai, Bhagalpur, Biharsharif, Buxar, Chaibasa, Chapra, Daltonganj, Darbhanga, Dhanbad, Dumka, Gaya, Giridih, Gopalganj, Gumla, Hajipur, Hazaribagh, Jamshedpur, Katihar, Madhubani, Motihari, Munger, Muzaffarpur, Nawada, Purnea, Ranchi, Saharsa, Samastipur, Sasaram, Sitamarhi, Siwan.
Delhi Circle : Delhi GPO, New Delhi, Indra Prastha, Ramesh Nagar, Sarojini Nagar, Lodi Road, Krishna Nagar, Ashok Vihar, Parliament Street, UPSC PO.
Gujarat Circle : Gandhinagar, Ahmedabad, Amreli Anand, Bharuch, Bhavnagar, Bhuj, Dahod, Godhra, Himatnagar, Jamnagar, Junagadh, Kheda, Mehesana, Navrangpura, Navsari, Palanpur, Patan, Porbandar, Rajkot, Revdi Bazar, Surat, Surendranagar, Valsad, Vadodara.
Haryana Circle : Ambala GPO, Ambala City, Bahadurgarh, Bhiwani, Faridabad, Gurgaon, Hissar, Jind, Karnal, Kurukshetra, Narnaul, Panipat, Rohtak, Sirsa, Sonepat.
Himachal Pradesh Circle : Shimla, Bilaspur, Chamba, Hamirpur, Kangra, Keylong, Kulu, Mandi, Nahan, Recong, Peo, Solan, Una.
Jammu & Kashmir Circle : Srinagar, Anantnag, Baramulla, Jammu, Kathua, Leh, Rajouri, Udhampur. Karnataka Circle : Bangalore GPO, Bangalore City, Basavangudi, HAL II Stage, Jayanagar, R.T. Nagar, Bagalkot, Raichur, Rajajinagar, Belgaum Bellary, Bidar, Bijapur, Chikmagalur, Chitradurga, Davengere, Dharwad, Gadag, Gulbarga, Hassan, Haveri, Hubli, Karwar, Kolar, Madikere, Mandya, Mangalore, Manipal, Mysore, Nanjagud, Shimoga, Sirsi, Tumkur, Udupi.
Kerala Circle : Trivandrum, Alleppey (Alappuzha), Calicut, Cannanore, Ernakulam, Kalpetta, Kasargod, Kattappana, Kottayam, Malappuram, Palghat, Pathanamthitta, Quilon, Trichur, Kavaratti, (Lakshadweep).
Madhya Pradesh Circle : Bhopal GPO, Bilaspur, Ambikapur, Balaghat, Betul, Bhind, Chhatarpur, Chhindwara, Damoh, Dewas, Dhar, Durg, Guna, Hoshangabad, Indore, Jabalpur, Jagdalpur, Jhabua, Khandwa, Khargone, Lashkar, Mandla, Mandsaur, Morena, Narsinghpur, Neemuch, Raigarh, Raipur, Raisen, Rajgarh (Biora), Rajnandgaon, Ratlam, Rewa, Sagar Cantt., Satna, Sehore, Seoni, Shahdol, Shajapur, Shivpuri, Sidhi, Tikamgarh, Ujjain, Vidisha.
Maharashtra Circle : Mumbai GPO, Andheri, Borivili, Chembur, Chinehbunder, Dadar, Girgaon, Kalbadevi, Mahim, Mandvi, Mumbai Central, Ahmednagar, Akola, Alibag, Amravati, Aurangabad, Beed, Bhandara, Buldhana, Chandrapur, Dhule, Jalagaon, Jalna, Karad, Kolhapur, Latur, Nagpur GPO, Nanded, Nasik, Osmanabad, Parbhani, Pune, Ratnagiri, Sangli, Satara, Sawantwadi, Solapur, Thane, Wardha, Yeotmal, Margaon (Goa), Panaji (Goa).
North East Circle : Agartala, Aizwal, Dharmanagar, Imphal, Itanagar, Kohima, Radhakishorepur, Shillong, Tura.
Orissa Circle : Bhubaneswar GPO, Angul, Bolangir, Balasore, Bargarh, Baripada, Berhamapur, Bhadrak, Bhawanipatna, Cuttack GPO, Dhenkanal, Jagatsinghpur, Jajpur, Jeypore (K), Jharsuguda, Kendrapara, Keonjhargar, Koraput, Nayagarh, Parlakhemundi, Phulbani, Puri, Rayagada, Sambalpur, Sundargarh.
Punjab Circle : Amritsar, Bhatinda, Faridkot, Ferozepur, Gurdaspur, Hoshiarpur, Jalandhar City, Kapurthala, Ludhiana, Moga, Patiala, Ropar, Sangrur, Chandigarh.
Rajasthan Circle : Jaipur GPO, Jawahar Nagar, Shastri Nagar, Ajmer, Alwar, Banswara, Baran, Barmer, Bharatpur, Bhilwara, Bikaner, Bundi, Chittorgarh, Churu, Dausa, Dholpur, Dungarpur, Hanumangarh, Hindaun, Jaisalmer, Jalore, Jhalawar, Jhunjhunu, Jodhpur, Kankroli, Kota, Nagaur, Pali Marwar, Sawaimadhopur, Shastri Circle Udaipur, Sikar, Sirohi, Sriganganagar, Tonk.
Tamil Nadu Circle : Chennai GPO, Anna Road, St. Thomas Mount, T. Nagar, Bodinayakanur, Chengalpattu, Chidambaram, Coimbatore, Cuddalore, Dharmapuri, Dindigul, Erode, Kanchipuram, Karur, Madurai, Nagapattinam, Nagercoil, Namakkal, Pudukottai, Ramanathapuram, Salem, Sivagangai, Tambaram, Thanjavur, Thiruvannamalai, Tiruchirapalli, Tirunelveli, Tiruvallur, Tiruvayur, Turaiyur, Tuticorin, Udhagamandalam, Vellore, Villupuram, Virudhunagar, Pondicherry.
Uttar Pradesh Circle : Lucknow, Lucknow Chowk, Agra, Akbarpur, Aligarh, Allahabad, Allahabad Katchery, Almora, Auraiya, Azamgarh, Bahraich, Ballia, Balrampur, Banda, Bansi, Barabanki, Bareilly, Basti, Bijnor, Budaun, Bulandshahr, Dehradun, Deoria, Dhampur, Etah, Etawah, Faizabad, Fatehgarh, Fatehpur, Firozabad, Ghaziabad, Ghazipur, Gonda, Gopeshwar, Gorakhpur, Haldwani, Hamirpur,Hardoi, Jaunpur, Jhansi, Kanpur, Kheri, Lalitpur, Mainpuri, Mathura, Mau, Meerut, Mirzapur, Moradabad, Muzaffarnagar, Nainital, Orai, Pauri, Padrauna, Pilibhit, Pithoragarh, Pratapgarh, Rai Bareli, Rampur, Roorkee, Saharanpur, Shahajahanpur, Sitapur, Sultanpur, Tehri, Unnao, Varanasi.
West Bengal Circle : Kolkata (Calcutta) GPO, Alipore, Barabazar, Beleghata, Belghoria, Cassipore, Park Street, Tollygunge, Balurghat, Bankura, Barasat, Berhampore, Burdwan, Chinsurah, Cooch Behar, Darjeeling, Howrah, Jalpaiguri, Krishnagar, Malda, Midnapore, Purulia, Suri, Siliguri, Port Blair (Andaman & Nicobar Islands), Gangtok (Sikkim).
Field Post Offices through Central Base Post Office (CBPO), 56 APO;
2 Central Base Post Office (CBPO) 99 APO.
Exam Details and Exam Centers
The examination is conducted according to the following plan
Part I - Written Examination carrying a maximum of 600 marks in the subject as shown below.
Part II - Personality Test carrying a maximum of 200 marks in respect of only those candidates who are declared qualified on the results of written examination.
1. The Subject of the Written Examination the time allowed and the maximum marks allotted to each subject are as follows:
Paper I - General Ability Test (English, General knowledge and Psychological Test) 2 hours and 200 marks.
Paper II - Physical science (Physics and Chemistry) 2 hours and 200 marks.
Paper III - Mathematics 2 hours and 200 marks
2. The papers in all the Subjects will consist of objective type questions only. The question papers ( Test Booklets) are set in English only.
3.In the question papers, wherever necessary, questions involving the Metric System of Weights and Measures only will be set.
4. Question Papers is approximately of the Intermediate standard.
5.Candidates must write the paper s in their own hand .In no circumstances are they allowed the help of a scribe to write the answers for them
6.The commission have discretion to fix qualifying marks in any or all the subjects as the examination.
7. The candidates are not permitted to use calculators or mathematical or Logarithmic tables for answering objective type papers (test Booklets). they should not, therefore .bring the same inside examination hall.
Personality Test - Personality Test carrying a maximum of 200 marks in respect of only those candidates who are declared qualified on the results of written examination. Each candidate will be interviewed by a Board who will have before them a record of his career both academic and extramural. They will be asked questions on matters of general interest. Special attention will be paid to assessing their potential qualities of leadership, initiative and intellectual curiosity, tact and other social qualities , mental and physical energy, power of practical application and integrity of character.
Exam centers
Agartala, Gangtok, Panaji (goa), Ahmedabad, Hyderabad, Patna, Aizwal, Imphal, Port blair, Allahabad, Itanagar, Raipur, Bangalore, Jaipur, Ranchi, Bareilly, Jammu, Sambalpur, Bhopal, Jorhat, Shillong, Chandigarh, Kochi, Shimla, Chennai, Kohima , Srinagar, Cuttack, Kolkata, Thiruvanathapuram, Dehradun, Lucknow, Tirupati, Delhi, Madurai, Udaipur, Dharwar, Mumbai, Vishakhapatnam, Dispur, Nagpur
Terms and Conditions of apprenticeship for special Class Apprentices selected through the Examination
The terms and conditions of Apprenticeship are as set out in the form of agreement prescribed in the Indian railway Establishment manual, brief particulars of which are given below:
Paper I
English
The questions will be designed to test the candidates' understanding and command of the language.
General Knowledge
The questions will be designed to test a candidate’s general awareness of the environment around him and its application to society. The standard of answers to questions should be as expected of students of standard 12 or equivalent.
a) Man and his Environment - Evolution of life, plants and animals, heredity and environment-Genetics, cells, chromosomes, genes. Knowledge of the human body-nutrition, balanced diet, substitute foods, public health and sanitation including control of epidemics and common diseases. Environmental pollution and its control. Food adulteration, proper storage and preservation of food grains and finished products, population explosion, population control. Production of food and raw materials. Breeding of animals and plants, artificial insemination, manures and fertilizers, crop protection measures, high yielding varieties and green revolution, main cereal and cash crops of India.
b) Solar system and the earth, Seasons, Climate, Weather, Soil-its formation, erosion Forests and their uses. Natural calamities cyclones, floods, earthquakes, volcanic eruptions. Mountains and rivers and their role in irrigation in India. Distribution of natural resources and industries in India. Exploration of under-ground minerals including Oil Conservation of natural resources with particular reference to the flora and fauna of India.
c) History, Politics and Society in India - Vedic, Mahavir, Budhdha, Mauryan, Sunga, Andhra, Kushan. Gupta ages (Mauryan Pillars, Stupa Caves, Sanchi, Mathura and Gandharva Schools, Temple architecture, Ajanta and Ellora). The rise of new social forces with the coming of Islam and establishment of broader contacts. Transition from feudalism to capitalism. Opening of European contacts. Establishment of British rule in India. Rise of nationalism and national struggle for freedom culminating in Independence.
d) Constitution of India and its characteristic features - Democracy, Secularism, Socialism, equality of opportunity and Parliamentary form of Government. Major political ideologies-democracy, socialism, communism and Gandhian idea of non-violence. Indian political parties, pressure groups, public opinion and the press, electoral system.
e) India’s foreign policy and non-alignment-Arms race, balance of power. World organisation-political, social, economic and cultural. Important events (including sports and cultural activities) in India and abroad during the past two years.
f) Broad features of Indian social system : The caste system, hierarchy - recent changes and trends. Minority social institution - marriage, family, religion and acculturation.
g) Division of labour, co-operation, conflict and competition, Social control - reward and punishment, art, law, customs, propaganda, public opinion, agencies of social control - family, religion, state educational institutions; factors of social change- economic, technological, demographic, cultural; the concept of revolution.
h) Social disorganization in India - Casteism, communalism, corruption in public life, youth unrest, beggary, drugs, delinquency and crime, poverty and unemployment.Social planning and welfare in India, community development and labour welfare; welfare of Scheduled Castes and backward classes.
i) Money - Taxation, price, demographic trends, national income, economic growth. Private and Public Sectors; economic and non-economic factors in planning, balanced versus imbalanced growth, agricultural versus industrial development; inflation and price stabilization, problem of resource mobilization. India’s Five Year Plans.
Psychological Test
The questions will be designed to assess the basic intelligence and mechanical aptitude of the candidate.
Paper-II
Physics
Length measurements using vernier, screw gauge, spherometer and optical lever. Measurement of time and mass.Straight line motion and relationships among displacement, velocity and acceleration, .Newton's laws of motion, Momentum, impulse, work, energy and power.Coefficient of friction.Equilibrium of bodies under action of forces. Moment of a force, couple. Newton’s law of gravitation. Escape velocity. Acceleration due to gravity.Mass and Weight; Centre of gravity, Uniform circular motion, centripetal force, simple Harmonic motion. Simple pendulum.Pressure in a fluid and its variation with depth. Pascal’s law. Principle of Archimedes. Floating bodies, Atmospheric pressure and its measurement.Temperature and its measurement. Thermal expansion, Gas laws and absolute temperature. Specific heat, latent heats and their measurement. Specific heat of gases. Mechanical equivalent of heat. Internal energy and First law of thermodynamics, Isothermal and adiabatic changes. Transmission of heat; thermal conductivity.Wave motion; Longitudinal and transverse waves. Progressive and stationary waves, Velocity of sound in gas and its dependence on various factors. Resonance phenomena (air columns and strings).
Reflection and refraction of light. Image formation by curved mirrors and lenses, Microscopes and telescopes. Defects of vision.Prisms, deviation and dispersion, Minimum deviation. Visible spectrum.Field due to a bar magnet, Magnetic moment, Elements of Earth’s magnetic field. Magnetometers. Dia, para and ferromagnetism.Electric charge, electric field and potential, Coulomb’s law.Electric current; electric cells, e.m.f. resistance, ammeters and voltmeters. Ohm’s law; resistances in series and parallel, specific resistance and conductivity. Heating effect of current.Wheatstone’s bridge, Potentiometer.Magnetic effect of current; straight wire, coil and solenoid electromagnet; electric bell.Force on a current-carrying conductor in magnetic field; moving coil galvanometers; conversion to ammeter or voltmeter.Chemical effects of current; Primary and storage cells and their functioning, Laws of electrolysis.Electromagnetic induction; Simple A.C. and D.C. generators. Transformers, Induction coil,Cathode rays, discovery of the electron, Bohr model of the atom. Diode and its use as a rectifier.Production, properties and uses of X-rays.Radioactivity; Alpha, Beta and Gamma rays.Nuclear energy; fission and fusion, conversion of mass into energy, chain reaction.
Chemistry
Physical Chemistry
Inorganic Chemistry
Brief Treatment of Elements and their industrially important compounds :
Hydrogen : Position in the periodic table. Isotopes of hydrogen. Electronegative and electropositive character. Water, hard and soft water, use of water in industries, Heavy water and its uses.
Organic Chemistry
Paper-III
Mathematics
1. Algebra :
Concept of a set, Union and Intersection of sets, Complement of a set, Null set, Universal set and Power set, Venn diagrams and simple applications. Cartesian product of two sets, relation and mapping - examples, Binary operation on a set - examples.
Representation of real numbers on a line. Complex numbers: Modulus, Argument, Algebraic operations on complex numbers. Cube roots of unity. Binary system of numbers, Conversion of a decimal number to a binary number and vice-versa. Arithmetic, Geometric and Harmonic progressions. Summation of series involving A.P., G.P., and H.P.. Quadratic equations with real co-efficients. Quadratic expressions: extreme values. Permutation and Combination, Binomial theorem and its applications.
Matrices and Determinants: Types of matrices, equality, matrix addition and scalar multiplication - properties. Matrix multiplication - non-commutative and distributive property over addition. Transpose of a matrix, Determinant of a matrix. Minors and Co-factors. Properties of determinants. Singular and non-singular matrices. Adjoint and Inverse of a square-matrix, Solution of a system of linear equations in two and three variables-elimination method, Cramers rule and Matrix inversion method (Matrices with m rows and n columns where m, n less than equal to 3 are to be considered).Idea of a Group, Order of a Group, Abelian group. Identitiy and inverse elements-Illustration by simple examples.
2. Trigonometry
Addition and subtraction formulae, multiple and sub-multiple angles. Products and factoring formulae. Inverse trigonometric functions - Domains, Ranges and Graphs. DeMoivre's theorem, expansion of Sin n0 and Cos n0 in a series of multiples of Sines and Cosines. Solution of simple trigonometric equations. Applications: Heights and Distance.
3. Analytic Geometry (two dimensions)
Rectangular Cartesian. Coordinate system, distance between two points, equation of a straight line in various forms, angle between two lines, distance of a point from a line. Transformation of axes. Pair of straight lines, general equation of second degree in x and y - condition to represent a pair of straight lines, point of intersection, angle between two lines. Equation of a circle in standard and in general form, equations of tangent and normal at a point, orthogonality of two cricles. Standard equations of parabola, ellipse and hyperbola - parametric equations, equations of tangent and normal at a point in both cartesian and parametric forms.
4. Differential Calculus
Concept of a real valued function - domain, range and graph. Composite functions, one to one, onto and inverse functions, algebra of real functions, examples of polynomial, rational, trigonometric, exponential and logarithmic functions. Notion of limit, Standard limits - examples. Continuity of functions - examples, algebraic operations on continuous functions. Derivative of a function at a point, geometrical and physical interpretation of a derivative - applications. Derivative of sum, product and quotient of functions, derivative of a function with respect to another function, derivative of a composite function, chain rule. Second order derivatives. Rolle's theorem (statement only), increasing and decreasing functions. Application of derivatives in problems of maxima, minima, greatest and least values of a function.
5. Integral Calculus and Differential equations :
Integral Calculus : Integration as inverse of differentiation, integration by substitution and by parts, standard integrals involving algebraic expression, trigonometric, exponential and hyperbolic functions. Evaluation of definite integrals-determination of areas of plane regions bounded by curves - applications.
Differential equations : Definition of order and degree of a differential equation, formation of a differential equation by examples. General and particular solution of a differential equation, solution of first order and first degree differential equation of various types - examples. Solution of second order homogeneous differential equation with constant co-efficients.
6. Vectors and its applications :
Magnitude and direction of a vector, equal vectors, unit vector, zero vector, vectors in two and three dimensions, position vector. Multiplication of a vector by a scalar, sum and difference of two vectors, Parallelogram law and triangle law of addition. Multiplication of vectors - scalar product or dot product of two vectors, perpendicularity, commutative and distributive properties. Vector product or cross product of two vectors - its properties, unit vector perpendicular to two given vectors. Scalar and vector triple products. Equations of a line, plane and sphere in vector form - simple problems. Area of a triangle, parallelogram and problems of plane geometry and trigonometry using vector methods. Work done by a force and moment of a force.
7. Statistics and probability :
Statistics : Frequency distribution, cumulative frequency distribution - examples. Graphical representation - Histogram, frequency polygon - examples. Measure of central tendency - mean, median and mode. Variance and standard deviation - determination and comparison. Correlation and regression.
Probability : Random experiment, outcomes and associated sample space, events, mutually exclusive and exhaustive events, impossible and certain events. Union and Intersection of events. Complementary, elementary and composite events. Definition of probability : classical and statistical - examples. Elementary theorems on probability - simple problems. Conditional probability, Bayes' theorem - simple problems. Random variable as function on a sample space. Binomial distribution, examples of random experiments giving rise to Binomial distribution.