Class notes used in Quantitative Techniques - I course at Praxis Business School, Calcutta

1. Probability Theory Q U A N T T E C H I N T E U Q I A S E V I T 1 0 S

6. State Space All Possible Outcomes Event A : Head Event B : Tail Event A : Identical Reading Event B : Different Reading Event A : Three Heads Event B : Two Heads Event C : Anything Else One Coin Tossed Two Coins Tossed Three Coins Tossed H T HH HT TH TT HHH HHT HTT THH HTH THT TTH TTT

7. Probability is NOT certainty ! H T T T T T H T T H P(H) = 0.5 Probability of getting H = 0.5 H H T T T H H H T H T T T T T H H T T T T H H H T H H T H T H H H H H T H H H T 3/10 3/10 6/10 9/20 2/10 11/30 6/10 17/40 8/10 25/50 T T H H T T H T H T 4/10 29/60 H T H H T T H H H T 6/10 499/1000 M a n y m o r e t r I a l s

23. Classical Definition of Probability When we choose a secretary, there are 100 possible outcomes .. But only 8 of these outcomes will give us a WOMAN DOCTOR

37. Probabilities under Statistical Dependence Conditional Probability P(B/A) = P(B A) / P(A) P(A/B) = P(B A) / P(B) Joint Probability P(B A) = P(B / A) x P(A) = P(A / B) X P(B)

44. Brand Conscious Customer : 1 Demographics tells us that P(A) = 0.2; P(B) = 0.8 We know the conditional probabilities P(S/A) = 0.6, P(S/B) = 0.1 Joint Probability of Sale and given type of customer hence P(SA) = P(S/A)xP(A) Marginal Probability of Sale is sum of the two joint probabilities P(S) = P(SA) + P(SB)