Question

An electrical engineer buys resistors from three different vendors. In the circuit in which he has designed, the resistors must meet a given power dissipation specification. Vendor A guarantees that 95% of their resistors meet the specifications. Vendor B guarantees that 98% of their resistors meet the specifications. Vendor C guarantees that 90% of their resistors meet the specifications. The engineer keeps the resistors form the three (3) vendors in three (3) separate boxes. He randomly selects one of the three boxes and from the randomly selected box; he randomly selects a resistor. It does not meet the specification What is the probability that the resistor came from vendor A. a) b) What is the probability that the resistor came from vendor B. What is the probability that the resistor came from vendor C

Answer 1

Plmekting specification I from vendor A) = 0.95 Plnot meeting specificationſ from vendor (A) = 0.05 Plmeeting specification. I from von doo B) = 0.98 Plnot meeting specification ( from vendor B) = 0.02 Plmeeting specification I from vendor c) = 0.90 Plnot meeting specification) from vendor c) = 0.10 Pl selecting a box) = I solved by Baye's theorem a) P(fromvendor Al defective resistor) 3) Pldefechrevesistoolfosmren dora) please continue to 1 The problem will be from a ven pl defective for Iscreetingbux 1 + pl defechrel from. I plselelting resistor I fromvendorf vendoA) (bxfrom rendorB) pl defective for Pl selecting box " Jenistur rends I from vendore.) 0.05x1 - 005:5 0 05 + 0.021 tolox! 0:17 17 Similarly 'Bland 'cl will be solved. by Pl. from vendor Bl defective. Presistor) = 0.02 605 x 1+0.07%) o loxol 0.7 - 4 = 0.02

c> pl from rendor el defective resistor) = 0.10^-3 0.05x1 + 0.01x! + 0.1084 017 19 0-10 = 10