In: Statistics and Probability
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 | 257 | 323 | 580 |
Passive | 485 | 95 | 580 |
Column Total | 742 | 418 | 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) = | |
P(S | A) = | |
P(S | Pa) = |
(b) Are the events S = sale and Pa = passive
approach independent? Explain.
Yes. The two events can occur together.
No. P(S) ≠ P(S | Pa).
Yes. P(S) = P(S | Pa).
No. The two events cannot 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) = |
(d) Compute P(N) and P(N |
A). (Enter your answers as fractions.)
P(N) = | |
P(N | A) = |
(e) Are the events N = no sale and A aggressive
approach independent? Explain.
No. The two events cannot occur together.
Yes. P(N) = P(N | A).
Yes. The two events can occur together.
No. P(N) ≠ P(N | A).
(f) Compute P(A or S). (Enter your answer as a
fraction.)
P(A or S) =