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.

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

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

   Round your answers to 3 digits after the decimal point.

   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?

   P(C1 | x1 = 1, x2 = 1) =

   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?

   P(C2 | x1 = 1, x2 = 1) =

   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?

   P(C1 | x1 = 0, x2 = 0) =

   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?

   P(C2 | x1 = 0, x2 = 0) =

   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?

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

   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?

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