22 July Mathematics

MATHEMATICS AFTERSCHOOOL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

MATHEMATICS Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

FIND THE PROBABILITY THAT THE BIRTHDAY OF RAM IS ON SUNDAY OR ON SATURDAY?  There

are 7 days in a week. Thus Sunday or Saturday would mean 2 days in a week. Probability is 2/7 answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

WHAT IS THE PROBABILITY OF GETTING A MULTIPLE OF 2 IN A TROW OF DICE?  There

are 6 possibilities : 1,2,3,4,5,6, in a dice. Out of these, multiples of 2 are : 2,4,6, thus probability is 3 out of 6.  Thus answer is 3/6 or ½ answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

What is the probability that in a throw of 2 dice, we get sum in even number? 







The total number of possibilities are : 6 * 6 = 36. We can have 18 such possibilities out of 36, when the sum is even. (half of 36). Examples: (1,1), (1,3), (1,5), (2,2), (2,4), (2,6), (3,1),(3,3),(3,5),(4,2),(4,4),(4,6),(5,1),(5,3),(5,5) ,(6,2),(6,4),(6,6) (count these – these are 18) The answer is 18 out of 36 or ½ answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

A bag contains 4 red, 5 blue, 6 black balls. We draw a ball. What is the probability that it is either red or blue?  Let

us count the total number of balls.  4+5+6 = 15.  Out of these 4 are red and 5 are blue – let us add these. (when we have OR in between, add these).  We get 9.  The probability is 9 out of 15 or 9/15 or 3/5 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

We draw 2 cards from a pack of cards. What is the probability that it is either a Jack or a Queen?  There

are total 52 cards in a card pack.  There are 4 Jacks and 4 queens.  Thus probability is 4+4 = 8 out of 52 or  8/52  Or 2/13 answer.  However, if we are drawing them one after another, the probability will be as under: 4C1 * 4C1 divided by 52 C 2. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Answer continued .. .  4C1

=  4*3*2*1 / 1* (4-1)! Or 3*2*1 = 4.  52 C 2 = 52! / 2! * (52-2)!  52*51/ 2*1 = 1326  Answer is 4*4 / 1326  =or 8 / 663 answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

In a shooting competition, the probability that A will hit the target is 2/3, B will hit the target is ¾ and C will hit the target is 4/5. what is the probability that the target is hit / hit by one of them?  Step

1. first find the possibility that the target is not hit at all.  It is : 1/3 * ¼ * 1/5 = 1/60.  Thus the probability that it will be hit is 11/60. = 59/60 (target is hit) www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Answer continued … …  Hit

by one only …  Hit by A : 2/3 * ¼ * 1/5 = 1/30  Hit by B : ¾ * 1/3 * 1/5 = 1/20  Hit by C : 4/5 * 1/3 * ¼ = 1/15  Thus probability that it is hit by one of them is : 1/30 + 1/20 + 1/15  = 90 / 600 or 3/20 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

A Box contains 6 blue balls and 3 red balls. Another box contains 4 blue and 5 red balls. We select 1 balls randomly, it is red, what is the probability?  Let

us assume that we select a box.randomly so its probability is ½  Red in first is 3 out of 9 = 3/9  Red in 2nd box is 5 out of 9 or 5/9.  Thus probability is : ½ * 3/9 and for second ½ * 5/9.  Total probability is : 3/18 + 5/18 or 8/18.(ans). www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

In a garden, 40% flowers are tulips and rest are roses. 25% of tulips and 10% of roses are red. What is the probability that a flower selected at random is red. And what is the probability that it is rose?  We

can find that 25% of 40 is 10 (tulip) and 10% of 60 is 6 (rose). thus 16 % flowers are red.  The probability that it is rose is 6/16 or 3/8 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Hulash and Rajesh try for CAT. The probability for Hulas getting IIM is 2/7 and for Rajesh is 3/8. what is the probability that both get through IIM?  When

we are trying for both (and), we have to multiply their probabilities.  Thus answer is 2/7 * 3/8  = 6/56 or 3/28 answer.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

An organising committee is to be formed for next Debate contest at AFTERSCHOOOL. The committee will consist of representatives from students (4 girls and 3 boys). What is the probability that in the committee of 3 persons, there are 2 girls?  7C3

(gives total possibility) =  (7*6*5*4*3*2*1)/(3*2*1*4*3*2*1)=5040/14 4 = 35 OR 7*6*5/3*2*1 = 35  Selecting 2 girls: 4C2 = 4*3/2*1 = 6  Answer is 6/35 answer. www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

ABO UT A FTERSCH OOO L Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Why such a programme? 







To promote people to take up entrepreneurship and help develop the society To enable people to take up franchising and other such options to start a business / social development project To enable people to take up social development as their mission To enable people to promote spirituality and positive thinking in the world

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Who are our supporters?  Afterschoolians,

our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us.  You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs     





Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee Option to take up part time job – so earn while you learn The only absolutely free course on internet

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Workshops from AFTERSCHOOOL         

IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Flexible Specialisations:          

Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Salient features: The only programme of its kind (in the whole world)  No publicity and low profile course  For those who want to achieve success in life – not just a degree  Indepth knowledge and expertise  Professional approac: World class approach  Strong intellectual and business capabilities  Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes  Scholarships for those from poor economic background  Latest and constantly changing curriculum – keeping pace with the time  Placement for those who are interested  Admissions open throughout the year  Latest and most advanced technologies, books and study www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS material 

Components              

Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Pedagogy          

Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) Rural development / Social welfare projects

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Branches  AFTERSCHOOOL

will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Case Studies  We

want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

Basic values at afterschoool        

Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help Ask fundamental questions : why, when, how & where? Embrace change – and compete with yourself only

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS

www.afterschoool.tk social entrepreneurship for better society

www.afterschoool.tk

AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS