Answer to Question #131565 in Statistics and Probability for Akshay Dileep

Question

14. A particular type of printer cartridge is produced by 2 companies – HP cartridge and Dell Cartridge. Suppose that HP produces 65 % of the cartridges and that dell produces 35 % of the cartridges. 8 % of the cartridges produced by HP are defective and 12 % of the Dell cartridges are defective. A customer purchases a new cartridge what is the probability that HP produced the cartridge? What is the probability that Dell produced the cartridge? The cartridge is tested and found to be defective. Now what is the probability that HP produced the cartridge? Or Dell produced the cartridge?

Answer 1

solutions

HP produces 65% of cartridges. The probability that HP produced the cartridge;$P(HP) = 0.65$

answer: 0.65

Dell produces 35% of cartridges. The probability that Dell produced the cartridge; $P(DELL) = 0.35$

answer: 0.35

Total defective cartridges are 8% of HP and 12% of DELL. Hence, probability that a cartridge picked is defective;

$$P(Defective)=(0.08× 0.65)+(0.12×0.35)$$ $$=0.094$$

Probability that the defective cartridge is HP produced

$$=\frac{P(defective \cap HP)}{P(defective)}=\frac{0.65×0.08}{0.094}$$

answer: 0.5532

Probability that the defective cartridge is DELL produced

$$=\frac{P(defective \cap Dell)}{P(defective)}=\frac{0.35×0.12}{0.094}$$

answer: 0.4468