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 278 302 580

Passive 493 87 580

Column Total 771 389 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),=

P(S|Pa). =

(Enter your answers as fractions.)

(b) Are the eventsS= sale andPa= passive approach independent? Explain.

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

No.P(S)P(S|Pa).

Yes. The two events can occur together.

No. The two events cannot occur together.

(c) ComputeP(A and S) andP(Pa and S). (Enter your answers as fractions.)P(A and S) =P(Pa and S) =

(d) ComputeP(N) andP(N|A). (Enter your answers as fractions.)P(N) =P(N|A) =

(e) Are the eventsN= no sale andAaggressive approach independent? Explain.

Yes. The two events can occur together.

Yes.P(N) =P(N|A).

No. The two events cannot occur together.

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

(f) ComputeP(A or S). (Enter your answer as a fraction.)

P(AorS) =