Answer to Question #121818 in Statistics and Probability for kantish

Question

A firm purchases a microchip used in the manufacturing of LED screens from four different suppliers. TechZone supplies 30 percent of the total microchips, Advance Electronics 25 percent, PSP importers 18 percent, and TechParts inc. 32 percent. TechZone tends to have the best quality, as only 3 percent of its microchips arrive defective. Advance Electronics chips are 4 percent defective, PSP importers chips are 7 percent defective, and Parts Inc. are 6.5 percent defective. a) If a random chip is selected, what is the probability that the chip is defective b) A defective chip was discovered in the latest shipment. What is the probability that it came from TechZone supplies? c) A defective chip was discovered in the latest shipment. What is the probability that it came from Parts Inc.?

Answer 1

P=(P(C).P(defective∣С))/((P(A).P(defective∣A)+(P(B).P(defective∣B)+(P(C).P(defective∣С))

P(TechZone )=0.30 

P(Advance Electronics)=0.25

P(PSP )=0.18 

P(TechParts )=0.32 

P(defective∣TechZone )=0.03

P(defective∣Advance Electronics)=0.04

P(defective∣PSP )=0.07

P(defective∣TechParts )=0.065

a)P=P(TechZone )*P(defective∣TechZone )+P(Advance Electronics)*P(defective∣Advance Electronics)+P(PSP )*P(defective∣PSP  )+P(TechParts )*P(defective∣TechParts )=0.30 *0.03+0.25*0.04+0.18 *0.07+0.32 *0.065=0.0524

b)P=P(TechZone )*P(defective∣TechZone )/(P(TechZone )*P(defective∣TechZone )+P(Advance Electronics)*P(defective∣Advance Electronics)+P(PSP )*P(defective∣PSP  )+P(TechParts )*P(defective∣TechParts ))=0.009/0.0524=0.17

c)P=P(TechParts )*P(defective∣TechParts )/(P(TechZone )*P(defective∣TechZone )+P(Advance Electronics)*P(defective∣Advance Electronics)+P(PSP )*P(defective∣PSP  )+P(TechParts )*P(defective∣TechParts ))=0.0208/0.0524=0.3969