Question

A manufacturer obtains clock-radios from three different subcontractors: 10% from A, 40% from B, and 50% from C. The defective rates for these subcontractors are 4%, 3%, and 3% respectively. If a defective clock-radio is returned by a customer, what is the probability that it came from subcontractor A? From B? From C? The probability that it came from subcontractor Ais (Type a decimal. Round to three decimal places if needed.) The probability that it came from subcontractor Bis (Type a decimal. Round to three decimal places if needed.) The probability that it came from subcontractor C is

Answer 1

Gaven that PCA) = 10% = 0.10 and P (DIA): 47=0.04 P(B)= 40 y = 0-40 P(DIB) = 34. -0.03 PCC)= 50% -0.50 PLD/C) = 3%=0.03. Where D= defective. the Total probability theorem, P(AP(DIA)+ P(B)P(PIB) + PCC)P(DI) = o loco.04) +0.40(0.03)+0. S0(0.03) using P (D) = = 0.031 : 0.10(0.04) -0... 129 0.031 using Bayes theorem, PLAID)= P(A) PODIA) P (D) P(BID) - PCB).P(DIB) PCD) 0.40(0.03) -0.387 0-03 1 0.4839. NO.484 * P(CD) - PCC). P(DC) 0.50 (0.03) 0.031 PID)