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Mar 18th, 2015

a. p_1 =P(<100K, audited) = 12/1000 = 0.012;   p_2 = P(>100K, audited) = 31/1000 = 0.031

b. P(x = 1) = (4 C 1)*p_1*(1-p_1)^3 = 4*0.012*0.988^3 = 0.0463 (rounded to 4 decimal places)

P(x > 1) = 1 - P(x=0) - P(x=1) =1 - (1-p_1)^4 -  (4 C 1)*p_1*(1-p_1)^3 = 1 - 0.95286 - 0.04629 = 0.0009

c. P(x = 1) = (4 C 1)*p_2*(1-p_2)^3 = 4*0.031*0.969^3 = 0.1128 (rounded to 4 decimal places)

P(x > 1) = 1 - P(x=0) - P(x=1) =1 - (1-p_2)^4 -  (4 C 1)*p_2*(1-p_2)^3 = 1 - 0.88165 - 0.11282 = 0.0055


Mar 18th, 2015

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