Answer to Question #234401 in Statistics and Probability for Maliha

Question

a firm purchased a micro chip used in the purchasing of LED screens from four different suppliers TechZone supplies 32 percent of the total micro chips, Advance Electronics 20 percent, PSP importers 23 percent,and Tech Parts inc 25 perfect .TechZone tends to have a best quality, as only 1 percent of its microchip arrive defective Advance Electronics chip are 3 percent defective,PSP importers chips are 6 percent defective and Part inc are 5.5 percent defective
a. if a random chips is selected ,what is the probability chips 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

Consider the following events:

D: the chip is defective,

TZ: the chip came from TechZone,

AE: the chip came from Advance Electronics,

PSP: the chip came from PSP,

TP: the chip came from Tech Parts inc.

a. By the Law of Total Probability

$$P(D)=P(TZ)P(D|TZ)+P(AE)P(D|AE)$$

$$+P(PSP)P(D|PSP)+P(TP)P(D|TP)$$

$$=0.32(0.01)+0.20(0.03)+0.23(0.06)+0.25(0.055)$$

$$=0.03675$$

b. By Bayes' Theorem

$$P(TZ|D)=\dfrac{P(D|TZ)P(TZ)}{P(D)}=\dfrac{0.01(0.32)}{0.03675}$$

$$\approx0.087075$$

c. By Bayes' Theorem

$$P(TP|D)=\dfrac{P(D|TP)P(TP)}{P(D)}=\dfrac{0.055(0.25)}{0.03675}$$

$$\approx0.374150$$