Probability 8 Sept
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PROBABILITY AFTERSCHO☺OL – 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
PROBABILITY Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
WHAT IS PROBABILITY? • Possibility of favourable events / total number of events. • For example: • I toss a coin and want to get Head, the probability is ½ • (because there are only two possibilities : Head and Tail). www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is highest probability? • 1 (when there is absolute certainity).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the least probability? • Zero • (when an event is impossible).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting an even number on tossing a dice? • Even numbers are: 2,4,6 • Thus there are 3 favourable possibilities, Total possibilities are 6 (1,2,3,4,5,6,) • Thus probability is 3 / 6 • Thus answer is ½.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting an odd number on tossing a dice? • Odd numbers are 1,3,5 • Thus there are 3 favourable possibilities, Total possibilities are 6 (1,2,3,4,5,6,) • Thus probability is 3 / 6 • Thus answer is ½.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What are the total number of possibilities if I toss a coin 4 times • The possibilities are as under: • H = Head, T = Tail • HHHH, HHHT, THTH,, HHTT, HTTT, TTTT, TTTH, TTHH, HTHT, HTTH,THHT,HTHH,THTT, HHTH,TTHT,THHH • OR • 2*2*2*2 = 2^4 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
I TOSS A DICE 2 TIMES, WHAT ARE THE TOTAL POSSIBILITIES? • THE POSSIBILITIES ARE : • 11,12,13,14,15,16,21,23,24,25,26,31,32,3 3,34,35,36,41,42,43,44,45,46,51,52,53,54 ,55,56,61,62,63,64,65,66 • THUS THERE ARE 36 POSSIBILITIES. • OR • 6^2 • OR 6*6 = 36 ANSWER. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A DICE IS ROLLED TWICE, WHAT IS THE PROBABILITY OF GETTING A DIFFERENCE OF 2 POINTS? `Q1@ • The total number of possibilities are 6*6 = 36. • The possibilities of difference of 2 are: • 13,24,35,46,31,42,53,64. • Thus there are 8 possibilities. Thus answer is 8/36 or 2/9 answer www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A DICE IS ROLLED THRICE, WHAT IS THE PROBABILITY OF GETTING A TOTAL OF 15 OR MORE? • The total number of possibilities are : 6*6*6 = 216 • Possibilities are: 666,665,656,566,556,565,655,664,646,46 6,555,654,645,456,465,564,546,663,636, 366, www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS • Answer = 20 / 216 .
A dice is thrown twice, what is the probability that we get 7 or more as total points? • Total number of possibilities = 36 • Total of 7 or more: 16,61,25,52,34,43,26,62,35,53,44,36,63,4 5,54,46,64,55,56,65,66 • Thus the total number of possibilities are 21 • Thus our answer is 21/36 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the chance of picking up a spade from a pack of cards? • There are 13 spades in a pack of playing cards. • There are 52 cards. • Thus the probability is 13/52 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting a 2 digit number which is divisible by 4 out of all 2 digit numbers? • • • •
Total number of 2 digit numbers are: (count from 10 to 99) 100 – 9 = 91 -1 = 90 100/4 gives you 25, which include 4,8,100, thus total number of 2 digit numbers divisible by 4 are 25 – 3 (4,8,100) = 22 • Answer = 22/90 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability that you form a 4 digit number from 2,3,5,7 and this number is divisible by 4? • Total number of 4 digit numbers are : 4*3*2*1 = 24 • The numbers divisible should have last 2 digits divisible by 4. The possibilities at the end are : 32,72, 52,. For each of these numbers, you have 2 more options, for example for 32, you have 5732 and 7532. Thus the probability is 6 (5732,7532,37527352,3572,7352) our of 24 or ¼ answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability that you form a 4 digit number from 2,3,5,7 and this number is divisible by 8? • The last 3 digits must be divisible by 8. thus the possibilities are : 752,352, • Thus there are two possibilities only. • Thus answer is 2 / 24 • =1/12 answer
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the chance of picking a spade or a king from a pack of cards? • There are 13 spades. There are 4 kings. • Thus there are 13+4 -1 (because one king is of spade itself). = 16 cards. • Thus there are total 52 cards. • Thus the answer is 16/52.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
ABOUT AFTERSCHO☺OL 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
About AFTERSCHO☺OL 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Workshops from AFTERSCHO☺OL • • • • • • • • •
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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's 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 • 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 material www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Branches • AFTERSCHO☺OL 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Basic values at AFTERSCHO☺OL • • • • • •
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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
PROBABILITY Dr. T.K. Jain.
AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
WHAT IS PROBABILITY? • Possibility of favourable events / total number of events. • For example: • I toss a coin and want to get Head, the probability is ½ • (because there are only two possibilities : Head and Tail). www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is highest probability? • 1 (when there is absolute certainity).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the least probability? • Zero • (when an event is impossible).
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting an even number on tossing a dice? • Even numbers are: 2,4,6 • Thus there are 3 favourable possibilities, Total possibilities are 6 (1,2,3,4,5,6,) • Thus probability is 3 / 6 • Thus answer is ½.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting an odd number on tossing a dice? • Odd numbers are 1,3,5 • Thus there are 3 favourable possibilities, Total possibilities are 6 (1,2,3,4,5,6,) • Thus probability is 3 / 6 • Thus answer is ½.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What are the total number of possibilities if I toss a coin 4 times • The possibilities are as under: • H = Head, T = Tail • HHHH, HHHT, THTH,, HHTT, HTTT, TTTT, TTTH, TTHH, HTHT, HTTH,THHT,HTHH,THTT, HHTH,TTHT,THHH • OR • 2*2*2*2 = 2^4 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
I TOSS A DICE 2 TIMES, WHAT ARE THE TOTAL POSSIBILITIES? • THE POSSIBILITIES ARE : • 11,12,13,14,15,16,21,23,24,25,26,31,32,3 3,34,35,36,41,42,43,44,45,46,51,52,53,54 ,55,56,61,62,63,64,65,66 • THUS THERE ARE 36 POSSIBILITIES. • OR • 6^2 • OR 6*6 = 36 ANSWER. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A DICE IS ROLLED TWICE, WHAT IS THE PROBABILITY OF GETTING A DIFFERENCE OF 2 POINTS? `Q1@ • The total number of possibilities are 6*6 = 36. • The possibilities of difference of 2 are: • 13,24,35,46,31,42,53,64. • Thus there are 8 possibilities. Thus answer is 8/36 or 2/9 answer www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
A DICE IS ROLLED THRICE, WHAT IS THE PROBABILITY OF GETTING A TOTAL OF 15 OR MORE? • The total number of possibilities are : 6*6*6 = 216 • Possibilities are: 666,665,656,566,556,565,655,664,646,46 6,555,654,645,456,465,564,546,663,636, 366, www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS • Answer = 20 / 216 .
A dice is thrown twice, what is the probability that we get 7 or more as total points? • Total number of possibilities = 36 • Total of 7 or more: 16,61,25,52,34,43,26,62,35,53,44,36,63,4 5,54,46,64,55,56,65,66 • Thus the total number of possibilities are 21 • Thus our answer is 21/36 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the chance of picking up a spade from a pack of cards? • There are 13 spades in a pack of playing cards. • There are 52 cards. • Thus the probability is 13/52 answer.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability of getting a 2 digit number which is divisible by 4 out of all 2 digit numbers? • • • •
Total number of 2 digit numbers are: (count from 10 to 99) 100 – 9 = 91 -1 = 90 100/4 gives you 25, which include 4,8,100, thus total number of 2 digit numbers divisible by 4 are 25 – 3 (4,8,100) = 22 • Answer = 22/90 www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability that you form a 4 digit number from 2,3,5,7 and this number is divisible by 4? • Total number of 4 digit numbers are : 4*3*2*1 = 24 • The numbers divisible should have last 2 digits divisible by 4. The possibilities at the end are : 32,72, 52,. For each of these numbers, you have 2 more options, for example for 32, you have 5732 and 7532. Thus the probability is 6 (5732,7532,37527352,3572,7352) our of 24 or ¼ answer. www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the probability that you form a 4 digit number from 2,3,5,7 and this number is divisible by 8? • The last 3 digits must be divisible by 8. thus the possibilities are : 752,352, • Thus there are two possibilities only. • Thus answer is 2 / 24 • =1/12 answer
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
What is the chance of picking a spade or a king from a pack of cards? • There are 13 spades. There are 4 kings. • Thus there are 13+4 -1 (because one king is of spade itself). = 16 cards. • Thus there are total 52 cards. • Thus the answer is 16/52.
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
ABOUT AFTERSCHO☺OL 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
About AFTERSCHO☺OL 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Workshops from AFTERSCHO☺OL • • • • • • • • •
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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's 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 • 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 material www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Branches • AFTERSCHO☺OL 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
AFTERSCHO☺OL's 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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
Basic values at AFTERSCHO☺OL • • • • • •
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
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
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