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 |
260 |
320 |
580 |
Passive |
466 |
114 |
580 |
Column Total |
726 |
434 |
1160 |
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.
1. Compute
P(S),P(S |A), andP(S |Pa). (Enter your answers as fractions.)
P(S) = ___
P(S |A) = ___
P(S |Pa) = ___
2. Are the events
S = sale andPa
= passive approach independent? Explain.
a. No. The two events cannot occur together.
b. Yes.
P(S) =P(S |Pa).
c. No.
P(S) ≠P(S |Pa).
d. Yes. The two events can occur together.
(c) ComputeP(A and S) andP(Pa and S). (Enter your answers as fractions.)
P(A and S) = ______
P(Pa and S) = _____
Extracted text: 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 260 320 580 Passive 466 114 580 Column Total 726 434 1160 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.) P(S) = 5/8 P(S | A) = P(S | Pa) = (b) Are the events S = sale and Pa = passive approach independent? Explain. O No. The two events cannot occur together. Yes. P(S) = P(S | Pa). O No. P(S) * P(S | Pa). O Yes. The two events can occur together. (c) Compute P(A and S) and P(Pa and S). (Enter your answers as fractions.) P(A and S) = P(Pa and S) =