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	277	303	580
Passive	471	109	580
Column Total	748	412	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. The two events cannot occur together. Yes. P(S) = P(S | Pa).     No. P(S) ≠ P(S | Pa). 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.

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

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

Answer 1

GIVEN:

The contingency table which displays the record of sales representatives who tried two approaches to selling a customer a new automobile: the aggressive approach and the passive approach for 1160 customers.

	Sale (S)	No sale (N)	Row total
Aggressive (A)	277	303	580
Passive (Pa)	471	109	580
Column total	748	412	1160

SOLUTION:

(a) Compute , , and :

Given that total number of customers

The probability of selling a new automobile is given by,

  

The probability of selling a new automobile is .

The probability of selling a new automobile given that aggressive approach was used is given by,

Let us first calculate the probabilityof selling a new automobile and aggressive approach used:

  

Next let us calculate the probability that an aggressive approach was used:

Now the probability of selling a new automobile given that aggressive approach was used is given by,

  

The probability of selling a new automobile given that aggressive approach was used is .

The probability of selling a new automobile given that passive approach was used is given by,

Let us first calculate the probabilityof selling a new automobile and passive approach used:

  

Next let us calculate the probability that passive approach was used:

      

Now the probability of selling a new automobile given that passive approach was used is given by,

  

The probability of selling a new automobile given that passive approach was used is .

(b) Are the events S = sale and Pa = passive approach independent?

The two events A and B are said to be independent if,

From part (a) we found that the probability of selling a new automobile given that passive approach was used is and the probability of selling a new automobile is .

Since is not equal to , the two events S = sale and Pa = passive approach are not independent. The two events can occur together.

(c) Compute and :

The probability of selling a new automobile and aggressive approach used is given by,

  

The probability of selling a new automobile and passive approach used is given by,

  

(d) Compute and :

The probability of not selling a new automobile is given by,

The probability of not selling a new automobile is .

The probability of not selling a new automobile given that aggressive approach was used is given by,

Let us first calculate the probability of not selling a new automobile and aggressive approach used:

  

Next let us calculate the probability that an aggressive approach was used:

Now the probability of not selling a new automobile given that aggressive approach was used is given by,

The probability of not selling a new automobile given that aggressive approach was used is .

(e) Are the events N = no sale and A aggressive approach independent?

The two events A and B are said to be independent if,

From part (d) we found that the probability of not selling a new automobile given that aggressive approach was used is and the probability of not selling a new automobile is .

Since is not equal to , the two events N = no sale and A aggressive approach are not independent. The two events can occur together.

(f) Compute :

The probability that aggressive approach was used or selling a new automobile is,

We know that the probability that an aggressive approach was used , the probability of selling a new automobile and the probability of selling a new automobile and aggressive approach used .

Using these probabilities in the formula given:

  

  

  

The probability that aggressive approach was used or selling a new automobile is .