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

ID: 3059195 • Letter: I

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. P(S) = P(S | Pa).

No. The two events cannot occur together.    

Yes. The two events can occur together.

No. 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.

No. The two events cannot occur together.

Yes. The two events can occur together.    

Yes. P(N) = P(N | A).

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 278 302 580 Passive 473 107 580 Column Total 751 409 1160

Explanation / Answer

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. P(S) = P(S | Pa).

No. The two events cannot occur together.    

Yes. The two events can occur together.

No. 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.

No. The two events cannot occur together.

Yes. The two events can occur together.    

Yes. P(N) = P(N | A).

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 278 302 580 Passive 473 107 580 Column Total 751 409 1160
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