Question

1. An accounting firm serves many companies (clients). Each client submits an annual financial report to the firm for auditing. The report may be fraudulent (denoted by class 1 or C1) or may be truthful (denoted by class 2 or C2). Each client may or may not have legal trouble before (denoted by x1) and may be of either small or large capital size (denoted by x2). Please compute the propensity of a new client submitting fraudulent report using the pivot tables below. Keep at least three digits after the decimal point.

Pivot table with C and x1.

	Prior Legal (x1 = 1)	No Prior Legal (x1 = 0)	Total
Fraudulent (C1)	55	65	120
Truthful (C2)	200	680	880
Total	255	745	1000

Pivot table with C and x2.

	Small (x2 = 1)	Large (x2 = 0)	Total
Fraudulent (C1)	100	20	120
Truthful (C2)	100	780	880
Total	200	800	1000

Compute the following probabilities.

P(x1 = 1 | C1)
P(x1 = 0 | C1)
P(x2 = 1 | C1)
P(x2 = 0 | C1)
P(x1 = 1 | C2)
P(x1 = 0 | C2)
P(x2 = 1 | C2)
P(x2 = 0 | C2)
P(C1)
P(C2)

Given a new client with legal trouble before (x1 = 1) with small size (x2 = 1), what is the propensity of this client submitting a fraudulent report?

Given a new client with legal trouble before (x1 = 1) with small size (x2 = 1), what is the propensity of this client submitting a truthful report?

Given a new client with no legal trouble before (x1 = 0) and large size (x2 = 0), what is the propensity of this client submitting a fraudulent report?

Given a new client with no legal trouble before (x1 = 0) and large size (x2 = 0), what is the propensity of this client submitting a truthful report?

Given a new client with no legal trouble before (x1 = 0) and small size (x2 = 1), what is the propensity of this client submitting a fraudulent report?

Given a new client with no legal trouble before (x1 = 0) and small size (x2 = 1), what is the propensity of this client submitting a truthful report?

Answer 1

Solutions for the probabilities are given below: