statistics & business problems 10 oct

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STATISTICS & BUSINESS PROBLEMS

AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME –

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OPEN FOR ALL FREE FOR ALL


STATISTICS & BUSINESS PROBLEMS

Dr. T.K. Jain.

AFTERSCHO☺OLCentre for social entrepreneurship

Bikaner M: 9414430763

[email protected]

www.afterschool.tk, www.afterschoool.tk


P(A) =3/5, P(B) = 2/3, P(AUB)=3/4, P(A/B) = ?

P(A∩B) = P(A)+P(B) -P(AUB)

=3/5 +2/3 – ¾

=19/15 – ¾

= (76 – 45) / 60

=31/60

31/60 DIVIDED BY 2/3 = 93/120

=.775 ANS.


P(A) AND P(B) ARE 2 INDEPENDENT EVENT, WHAT IS

P(AUB), IF P(A) = 3/5 AND P(B)=2/3?

• P(AUB) = P(A) +P(B) – P(A) *P(B)

• =3/5+2/3 – (3/5*2/3)

• =19/15 – 6/15

• =13/15 answer.


2X+3Y+4 = 0, Variance of X = 6, what is variance of Y?

• Let us take standard deviation of X that is : 2.449

• Now put this value in place of X and we have a new equation :

• 2X = 3Y (ignore constant and put these as equal).

• 2*2.449 = 3Y

• Y = 1.632, square it: 2.6667 answer


A box contains 5 white and 7 black balls. Two successive draws of 3 balls are made with replacement,

what is the probability that first draw will produce white and 2nd draw will produce black balls?

• 5c3/12c3 * 7c3/12c3• =(fact(5)/(fact(2)*fact(3)))/(fact(12)/(fact(3)*fact(9)))

=.0454 • =(fact(7)/(fact(4)*fact(3)))/(fact(12)/(fact(3)*fact(9)))

=.15 multiply them • =.15*.045 =.0072 answer


A box contains 5 white and 7 black balls. Two successive draws of 3

balls are made without replacement, what is the probability

that first draw will produce white and 2nd draw will produce black

balls?• 5c3/12c3 * 7c3/9c3• =(fact(5)/(fact(2)*fact(3)))/(fact(12)/(fact(3)*fact(9)))

=.0454 • =(fact(7)/(fact(4)*fact(3)))/(fact(9)/(fact(3)*fact(6)))

=.416 Now multiply them • =.416*.045 =.0189 answer


Fit a binomial distribution in the following data?

X Frequency

Expected

difference

0 4 2.3 .092

1 6 7.29 .29.

2 8 11.25 .45

3 5 5 .20

4 2 1.025 .041

Total 25 &fx 45


Solution

• Average = 45/25 = 1.8• Divide 1.8 by 4 = .45• Now put the formulae: • NCR *(.45)^r *(.55)^(n-r)• = 4c0*(.45)^0*(.55)^4 =.092• = 4c1*(.45)^1*(.55)^3 =.29• = 4c2*(.45)^2*(.55)^2 =.45• =4c3*(.45)^3*(.55)^1=.20• = 4c4*(.45)^4*(.55)^0=.041


P(A) =1/3, P(B) = ½, P(A-B) = 1/5, what is the probability that only B

will happen?

• P(A) = 1/3 (WHICH INCLUDES A+B ALSO).

• P(A-B) = 1/5 (ONLY A – BECAUSE HERE B IS EXCLUDED)

• P(A &B) (Together) = 1/3-1/5 = 2/15

• P(ONLY B) = ½ - 2/15 = 11/30 ans.


ABOUT AFTERSCHO☺OL

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Why such a programme?

• To promote people to take up entrepreneurship and help develop the society

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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.


About AFTERSCHO☺OL PGPSE – the best programme for developing great

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Workshops from AFTERSCHO☺OL

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Components • Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

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• 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.


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• 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.


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and help • Ask fundamental questions : why, when, how &

where?• Embrace change – and compete with yourself

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