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:

	Sale	No Sale	Row Total
Aggressive	256	324	580
Passive	466	114	580
Column Total	722	438	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.

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.)

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

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

Answer 1

Consider the events

A: Aggressaive approach.

Pa : Passive approach.

S : Sale

N : No sale.

From the table

n = Total number of participating customers.

n(A) = 580, n(Pa) = 580, n(s) = 722, n(N) =438

a)

By definition of conditional probability

b) If the sale and Passive approach is independent if

Here

Hence S and Pa are not independent.

Correct Answer - No, Two event can Occur together.

c)

d)

By definition of conditional probability

e) Since P(N) # P(N/A)

Hence they are not independent.

Correct Answer -Correct Answer - No , Two event can Occur together.

f) By addition theorem

.