Probability
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This material is a part of our PGPSE programe. Our programme is available for any student after class 12th / graduation. AFTERSCHO☺OL conducts PGPSE, which is available free to all online students. ...

This material is a part of our PGPSE programe. Our programme is available for any student after class 12th / graduation. AFTERSCHO☺OL conducts PGPSE, which is available free to all online students. There are no charges. PGPSE is a very rigorous programme, designed to give a comprehensive training in social entrepreneurship / spiritual entrepreneurship. This programme is aimed at those persons, who want to ultimately set up their own business enterprises which can benefit society substantially. PGPSE is a unique programme, as it combines industry consultancy, business solutions and case studies in addition to spirituality and social concerns. You can read the details at www.afterschoool.tk or at www.afterschool.tk

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Probability Presentation Transcript

  • 1. 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
  • 2. PROBABILITY Dr. T.K. Jain. AFTERSCHO ☺ OL Centre for social entrepreneurship Bikaner M: 9414430763 [email_address] www.afterschool.tk , www.afterschoool.tk www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS
  • 3. WE DRAW THREE CARDS FROM A PACK OF CARDS WITHOUT REPLACEMENT, WHAT IS THE PROBABILITY THAT THEY ARE OF BLACK COLOUR?
    • There are 26 cards which are black and 26 red cards in a pack of cards. Thus probability of the first card being black is : 26/52. Similarly, the probabilty of the second card is : 25/51 (as card is not replaced), similarly, the probability for the third card : 24/50.
    • Probability of first 3 cards being black:
    • 26/52*25/51*24/50= .117 answer.
  • 4. WE DRAW THREE CARDS FROM A PACK OF CARDS WITH REPLACEMENT, WHAT IS THE PROBABILITY THAT THEY ARE OF BLACK COLOUR?
    • There are 26 cards which are black and 26 red cards in a pack of cards. Thus probability of the first card being black is : 26/52. Similarly, the probabilty of the second card is : 26/52 (as the card which has been drawn, has been replaced). The probability for the third card is also: 26/52 (as we again replace the card being drawn).
    • Thus probability of the first 3 cards being black :
    • = 26/52*26/52*26/52 = .125 answer.
  • 5. P(a) =1/2, P(b) = 1/3, P(a ∩b)=1/4, what is P (aUb)?
    • As we can see the union of a + b =
    • ½ + 1/3 – ¼
    • = .583 answer.
    1/2 1/3 1/4
  • 6. P(a) =1/2, P(b) = 1/3, P(a ∩b)=1/4, what is P (a/b)?
    • It means the probability of a, when b has already taken place. It is calculated by dividing P(a ∩b) by P(b)
    • Therefore, the probability will be calculated as : ¼ divided by 1/3
    • Thus we have .25/ .33 = .75 answer.
  • 7. P(a) =1/2, P(e) = 1/3, P(a ∩e)=1/4, what is P (ā∩ē)
    • Here we have to identify ā and ē. It is the area, which neither belongs to a nor to b. ā is equal to 1- ½ = ½. ē is equal to 1-1/3 , which is 2/3. there intersection is :
    • 1 – P (aUb)
    • =1 - .583
    • =.417 answer.
  • 8. About AFTERSCHO☺OL
    • PGPSE - World’s most comprehensive programme on social entrepreneurship – after class 12 th
    • Flexible – fast changing to meet the requirements
    • Admission open throughout the year
    • Complete support from beginning to the end – from idea generation to making the project viable.
  • 9. Branches of AFTERSCHO☺OL
    • PGPSE programme is open all over the world as free online programme.
    • Those who complete PSPSE have the freedom to start branches of AFTERSCHO☺OL
    • A few branches have already started - one such branch is at KOTA (Rajasthan).
  • 10. Workshop on social entrepreneurship
    • We conduct workshop on social entrepreneurship – all over India and out of India also - in school, college, club, association or any such place - just send us a call and we will come to conduct the workshop on social entrepreeurship.
    • These workshops are great moments of learning, sharing, and commitments.
  • 11. FREE ONLINE PROGRAMME
    • AFTERSCHO☺OL is absolutely free programme available online – any person can join it. The programme has four components :
    • 1. case studies – writing and analysing – using latest tools of management
    • 2. articles / reports writing & presentation of them in conferences / seminars
    • 3. Study material / books / ebooks / audio / audio visual material to support the study
    • 4. business plan preparation and presentations of those plans in conferences / seminars
  • 12. 100% placement / entrepreneurship
    • AFTERSCHO☺OL has the record of 100% placement / entrepreneurship till date
    • Be assured of a bright career – if you join AFTERSCHO☺OL
  • 13. Pursue professional courses along with PGPSE
    • AFTERSCHO☺OL permits you to pursue distance education based professional / vocational courses and gives you support for that also. Many students are doing CA / CS/ ICWA / CMA / FRM / CFP / CFA and other courses along with PGPSE.
    • Come and join AFTERSCHO☺OL