In a sales effectiveness seminar, a group of sales representatives tried a few approaches to selling a new automobile to a customer: the aggressive approach, the passive approach and a mixture of both. For 1740 customers, the following record was kept:

Sale No Sale Total
Aggressive 265 315 580
Passive 481 99 580
Column 746 414 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 I A), and P(S | Pa). (Enter your answers as fractions.)

1. P(S) = 373/580

2. P(S|A) = 53/116

3. P(S|Pa) = 481/580

Step-by-step explanation:

Given

Sale No SaleTotal

Aggressive 265 315 580

Passive 481 99 580

Total 7464141160

A = aggressive approach,

Pa = passive approach,

S = sale,

N= no sale.

(a) Computing P(S)

This is calculated as the division of customers that participated in sales by total customers

Customers that participated in sales = 265 + 481 = 746

Total Customers = 1160

P(S) = 746/1160

P(S) = 373/580

b.

P(S|A) means that the probability that a sales occur given that the aggressive method was used.

To solve this, we check the cell where Sales and Aggressive intersect

The cell element = 265

Total = 580

P(S|A) = 265/580

P(S|A) = 265/580

P(S|A) = 53/116

c.

P(S|Pa) means that the probability that a sales occur given that the passive method was used.

To solve this, we check the cell where Sales and Passive intersect

The cell element = 481

Total = 580

P(S|Pa) = 481/580

answer: the equation matches the regression

step-by-step explanation: