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	290	290	580
Passive	488	92	580
Column Total	778	382	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. The two events can occur together.

No. The two events cannot occur together.

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

(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.

Yes. 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) = ______