The following information has been found by analysing past tax return data. 10%

ID: 3048905 • Letter: T

Question

The following information has been found by analysing past tax return data.

10% of tax returns are fraudulent;

45% of fraudulent tax returns contain more than 5 deductions; and

5% of legitimate (not fraudulent) tax returns contain more than 5 deductions.

Use the following definition to answer the questions below.

F = Tax return is fraudulent

D = Tax return contains more than 5 deductions

a) Calculate P(FC)

b) Calculate P(DF)

c) Calculate P(DFC)

d) Calculate P(D)

e) Calculate P(F|D)

f) Are F and D mutually exclusive? Justify your answer.

g) Are F and D independent? Justify your answer.

P(F) = 0.1, P(D|F) = 0.45, P(D|FC) = 0.05

a) P(FC) = 1-P(F) = 1-0.1 = 0.9

b) P(D) = P(D|F)P(F)

P(D) = 0.45*0.1= 0.045

c) P(D and FC) = P(D|FC)P(FC) = 0.05*0.9 = 0.045

d) P(D) = P(D|F)P(F) + P(D|FC)P(FC)

P(D) = 0.45*0.1 + 0.05*0.9 = 0.045 + 0.045 = 0.09

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