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.

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

(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. P(N) P(N | A).No. The two events cannot occur together.

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

Sale No Sale Row Total Aggressive 290 290 580 Passive 477 103 580 Column Total 767 393 1160

Explanation / Answer

(a) P(S) = 767/ 1160

P(S|A) = 290/580 = 1/2

P(S|Pa) = 477/580

(b) P(S) = 767/1160 and P(S|Pa) = 477/580 and the two are not equal.

  No. P(S) P(S | Pa)

(c) P(A and S) = 290/1160 = 1/4

P( Pa and S) = 477/1160

(d) P(N) = 393/1160

P(N| A) = 290/580 =1/2

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

(f) P(A or S) = P(A) + P(S) - P(A and S)

= 580/1160 + 767/1160 - 290/1160

= 1057/1160

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