Problem 2 (8 points) In a sales effectiveness seminar, a group of sales represen

Question

Problem 2 (8 points) In a sales effectiveness seminar, a group of sales representatives tried two approaches to selling a customer a new automobile: the aggressive approach and the passive approach. For 1160 customers, the following record was kept. Sale No Sale Row Total Aggressive 289 29 580 Passive Column Total 783 377 1160 494 86 580 Suppose a customer is selected at random from the 1160 participating customers. Let us use the following notation for events. A = aggressive approach, Pa-passive approach, S= sale, N= no sale. So, P(A) is the probability that an aggressive approach was used, and so on. (Enter your answers as fractions.) a) Compute P(S), P(S| A), and P(S| Pa) b) Compute P(N) and P(N|A). Are N and A independent? Explain using a formula. c) Compute P(A o S).

Explanation / Answer

a)P(S) =783/1160 =0.675

P(S|A) =289/580=0.4983

P(S|Pa) =494/580 =0.8517

b)P(N) =377/1160=0.325

and P(N|A) =291/580 =0.5017

as P(N) is not equal to P(N|A) ; tehrefore N is not independent of A. ( Note:here as P(N|A) =P(N n A)/P(A) for independnece P(N n A) =P(N)*P(A) ; therefore P(N|A) should be equal to P(N) which is not here; hence not indepednent)

c)P(A or S) =(289+291+494)/1160=1074/1160=0.9259

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