Quantitative techniques for entrepreneurs


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This material is for PGPSE / CSE students of AFTERSCHOOOL. PGPSE / CSE are free online programme - open for all - free for all - to promote entrepreneurship and social entrepreneurship PGPSE is for those who want to transform the world. It is different from MBA, BBA, CFA, CA,CS,ICWA and other traditional programmes. It is based on self certification and based on self learning and guidance by mentors. It is for those who want to be entrepreneurs and social changers. Let us work together. Our basic idea is that KNOWLEDGE IS FREE & AND SHARE IT WITH THE WORLD

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Quantitative techniques for entrepreneurs

  1. 1. QUANTITATIVE TECHNIQUES FOR ENTREPRENEURS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india FOR – PGPSE / CSE PARTICIPANTS mobile : 91+9414430763
  2. 2. My words.... Here I present a few basic questions on quantitative techniques. I wish that more people should become entrepreneurs. An ordinary Indian entrepreneur wishes to remain an honest entrepreneur and contribute to the development of nation but we have to strengthen those institutions which truly promote entrepreneurship, not just degree granting institutions. Let us work together to promote knowledge, wisdom, social development and education. We believe in free education for all, free support for all, entrepreneurship opportunities and training for all. Let us work together for these goals. ... I alone cant do much, I need support of perosns like you .......... ...
  3. 3. What is the probability that the product of three consecutive integers will be a multiple of 12? Consecutive = continuous like 1,2,3,4,5,6,7 .. if the three numbers start with even number then it will be dividible by 12 but if it starts with an odd number then it will not be divisible by 12. thus the probability is ½ ( as even and odd numbers are in equal number) .
  4. 4. If there are 35 students in your class, and four students will be chosen to give a presentation each day until everyone has made a presentation what is the probability that you will be chosen to make your presentation the first day? 4/35 answer
  5. 5. If you have not been chosen by the fourth day, what is the probability that you will be chosen the first on the fourth day? (35-12) = 23 =1/23 answer
  6. 6. If you have not been chosen by the fourth day, what is the probability that you will be chosen on the fourth day? 4/23
  7. 7. A square target 15 cm on a side contains 40 non-overlapping circles each 2 cm in diameter. Find the probability that a dart thrown at random hits one of the circles. Area on square = 15*15 = 225 area of circle = 22/7 * 1 * 1= 3.142857 total area on circles 3.1428 * 40 = 125.71 probability = 125.7/ 225 =.558 answer
  8. 8. In cooking class, 1 out of 5 souffles that Jigyasa makes will collapse. She is preparing 6 souffles to serve at a party for her parents. What is the probability that exactly 4 of them do not collapse? Ncrp^rq^(n-r) = 6c2(1/5)^2*(4/5)^4 answer
  9. 9. A stockbroker is researching 13 independent stocks. An investment in each stock will either make money or lose money. The probability that each stock will make money is 5/8. What is the probability that exactly 10 of the stocks make money? Ncr*p^r*q^(n-r) = 13c10(5/8)^10*(3/8)^3 answer
  10. 10. On an assembly line of Acme Radio, the probability that a radio is defective is 1/15. If an inspector randomly checks 10 items, what is the probability of finding exactly 2 defective Ncr*p^r*q^(n-r) = 10c2(1/15)^2*(14/15)^8 answer
  11. 11. An auto insurance company charges younger drivers a higher premium than it does older drivers because younger drivers as a group tend to have more accidents. The company has 3 age groups: Group A includes those under 25 years old, 22% of all its policyholders. Group B includes those 25-39 years old, 43% of all its policyholders, Group C includes those 40 years old and older. Company records show that in any given one-year period, 11% of its Group A policyholders have an accident. The percentages for groups B and C are 3% and 2%, respectively. What percent of the company’s policyholders are expected to have an accident during the next 12 months? 11% of 22% + 3% of 43% + 2% of 35% =4.41% answer
  12. 12. How many different baseball teams of nine players can Jain High School put on the field if they have 2 players that can only play catcher, 6 players that can only be pitchers, and 17 that can play any of the other seven positions? 2c1*6c1*17c7 answer
  13. 13. In how many ways can a committee of 5 people be chosen from a group of 6 women and 7 men if the committee must consist of 3 women and 2 men. 6c3 * 7c2 answer
  14. 14. You put Rs 500 into the pocket of one of 6 pockets in your jeans, but you cannot remember which pocket. What is the probability that you find the money in the first pocket that you check? After checking two pockets without success, what is the probability that the Rs500 will be in the next pocket you check? First pocket = 1/6 after checking 2 pockets : answer = ¼ answer
  15. 15. A weather station in a certain area gathers data about the chance of precipitation. It predicts that, if it rains on a given day, 50% of the time it will rain on the next day. If it is not raining it will rain on the next day only 30% of the time. The weather forecast for Monday predicts the chance of rain 80%. Find the chance of rain on Wednesday using this pattern. Rain on M,T,W : .8*.5*.5 = .2 Rain on M,W = .8*.5*.3 = .12 Rain on T,W = .2*.5*.5 = .05 Rain on W = .2*.5*.3 = .03 total = .4 answer
  16. 16. Suppose you have forgotten you locker combination. There are 36 numbers on the lock, and the correct combination order is right __ - left __ - right __. How many combinations may be necessary to try in order to open the lock? There are 3 spaces so we need 3 digits out of 36, so we have to pick up 3 out of 36 the numbers may be repeated so : 36* 36*36 answer
  17. 17. Gajendra's Lottery has 6 numbers out of 48 are drawn at random. The proceeds from the lottery help finance educational programs in the state. What is the probability of winning one of the weekly Lotto drawings if you buy one ticket? 48p6 answer
  18. 18. Gajendra's security code is a system of dots and dashes, and spaces that telegraphers in India once used to send messages by wire. How many different arrangements are there of 7 dots, 3 dashes, and 2 spaces? 7*3*2 answer
  19. 19. What is the sum of this series for first 8 terms ? 1,2,4,8.... This is GP formula for sum of GP = A (R^N -1) / (R-1) =1 ( 2^8 – 1) / ( 2 -1 ) = 255 ANSWER
  20. 20. What is the ratio of 3 score to 4 dozen ? Score = 20, dozen = 12 so ratio is : (3*20) : (4*12) 60:48 or 5:4 answer
  21. 21. A box contains 6 red 7 white and 4 blue balls. The number of selections of 3 balls can be made so that one is of each colour is ? 6c1*7c1*4c1 =6*7*4 = 168 answer
  22. 22. A bag contains 6 white and 4 black balls .Two balls are drawn at random .Find the probability that they are of the same colour? EITHER WHITE : 6C2 OR BLACK 4C2 =15+6 =21 ANSWER
  23. 23. Two dice are thrown together .What is the probability that the sum of the number on the two faces is divisible by 4 or 6? Multiples of 4 or 6 are : 4,6,8,12 when we toss two dice, we have 36 total possibilities. Out of these the relevance possibilities are : for four : 13, 22, 31, for 6: 15,24,33,42,51, for 8 = 26,35, 44,53,62 for 12 : 6,6 thus answer is : 14/36 answer
  24. 24. Two cards are drawn at random from a pack of 52 cards What is the probability that either both are black or both are queens? Probability that both are black : 26/52 * 25/51 or Probability that both are queen : 4/52 * 3/51 add them = .241 answer
  25. 25. Two diced are tossed the probability that the total score is a prime number? Total score will be a prime number if it is : 2,3,,5,7,,11 the combinations are : 11, 12,21,14,23,32,16,25,34,43,4152,61,56,65 =15/36
  26. 26. Download links .... http://www.scribd.com/doc/30778316/Permutations-and-Combinations http://www.scribd.com/doc/30778304/Differentiation-and-Integration http://www.scribd.com/doc/30778217/Unitary-Methods http://www.scribd.com/doc/30778090/Questions-on-Volume-and-Surface-Area-for-Aptitude-Tests http://www.scribd.com/doc/30646219/Mock-Interview-for-Banking http://www.scribd.com/doc/30888753/General-Knowledge-and-Current-Affairs
  27. 27. Download links .... http://www.scribd.com/doc/30778316/Permutations-and-Combinations http://www.scribd.com/doc/30778304/Differentiation-and-Integration http://www.scribd.com/doc/30778217/Unitary-Methods http://www.scribd.com/doc/30778090/Questions-on-Volume-and-Surface-Area-for-Aptitude-Tests http://www.scribd.com/doc/30646219/Mock-Interview-for-Banking http://www.scribd.com/doc/30888753/General-Knowledge-and-Current-Affairs
  28. 28. Download links ..... http://www.scribd.com/doc/30646577/Afterschoool-Model http://www.scribd.com/doc/11953346/Mathematics-for-Fms-Cat-GMAT-GRE-Bank-Po-RmatUpmatCetXat2 http://www.scribd.com/doc/11867744/Management-Aptitude-Test-for-CatGMATCetUpmatRmatXat http://www.brijj.com/group/gmat-entrance-exam--presentation--Advanced-Mathematics-For-Gmat-Cat-Mat?eid=306563 http://www.docstoc.com/docs/3921499/ENGLISH-%E2%80%93-ERROR-SPOTTING-AND-SENTENCE-IMPROVEMENT http://www.docstoc.com/docs/3967158/basiC-MATHEMATICS-for-CAT-GMAT-MAT/ http://www.authorstream.com/Presentation/tkjainbkn-146787-mathematics-openmat-mat-cat-gmat-law-mba-management-business-research-cfp-cfa-frm-cpa-ca-cs-icwa-india-rajasthan-entertainment-ppt-powerpoint/ http://www.authorstream.com/Presentation/tkjainbkn-146773-mathematics-gmat-cat-mat-xat-rmat-law-mba-management-business-research-cfp-cfa-frm-cpa-ca-cs-icwa-india-rajasthan-advanced-mat2-education-ppt-powerpoint/
  29. 29. Spread the concepts of AFTERSCHOOOL Join PGPSE start CENTRES of AFTERSCHOOOL spread entrepreneurship & social entrepreneurship let us work for social upliftment together let us work for some common goals conduct workshops on social entrepreneurship make your career in social entrepreneurship