In a sales effectiveness seminar, a group of sales representatives tried two app

Question

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:

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.

(a) Compute P(S), P(S | A), and P(S | Pa). (Enter your answers as fractions.)

(b) Are the events S = sale and Pa = passive approach independent? Explain.

Yes. The two events can occur together.No. The two events cannot occur together.    No. P(S) ? P(S | Pa).Yes. P(S) = P(S | Pa).

(c) Compute P(A and S) and P(Pa and S). (Enter your answers as fractions.)

(d) Compute P(N) and P(N | A). (Enter your answers as fractions.)

(e) Are the events N = no sale and A aggressive approach independent? Explain.

Yes. P(N) = P(N | A).Yes. The two events can occur together.    No. The two events cannot occur together.No. P(N) ? P(N | A).

(f) Compute P(A or S). (Enter your answer as a fraction.)
P(A or S) =

Sale No Sale Row Total Aggressive 286 294 580 Passive 470 110 580 Column Total 756 404 1160

Explanation / Answer

a) P(S) = 756/1160

= 189/290

P(S | A) = 286/580

= 143/290

P(S | Pa) = 470/580

= 47/58

b) No. P(S) ? P(S| Pa)

c) P(A&S) = 286/1160

= 143/580

P(Pa & S) = 470/1160

= 47/116

d) P(N) = 404/1160

= 101/290

P(N | A) = 294/580

= 147/290

e) No. P(N) ? P(N | A)

f) P(A or S) = (580+470)/1160

= 1050/1160

= 105/116

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