There are three companies that produce a critical electronic navigation component (ENC) used in the aerospace industry. These companies are Alice Manufacturing, Byte International, and Cognizant Technologies. Alice makes 85% of the ENCs, Byte makes 10%, and Cognizant makes the remaining 5%. The ENCs made by Alice have a 2.5% rate of defects, the ones made by Byte have a 4.0% rate of defects, and the ones made by Cognizant have a 6% rate of defects. If an ENC is randomly selected from the general population of ENCs, the probability that it was made by Alice is _. If this ENC is later tested and found to be defective, the probability that it was made by Alice is _.

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okpalawalter8 okpalawalter8 · Answer 1 · 2020-10-13T13:29:03+02:00

Answer:

a

[tex]P(A) = 0.85[/tex]

b

[tex]P(A | D) = 0.7522 [/tex]

Step-by-step explanation:

From the question we are told that

The percentage of ENC made by Alice is P(A) 85% = 0.85

The percentage of ENC made by Byte P(B) 10%=0.10

The percentage of ENC made by Cognizant P(C) = 5%= 0.05

The percentage rate of defect of ENC made by Alice is p = 2.5 % = 0.025

The percentage rate of defect of ENC made by Byte is q = 4.0% = 0.04

The percentage rate of defect of ENC made by Cognizant r = 6% =0.06

Generally the probability that a randomly selected ENC will be made by Alice is

[tex]P(A) = 0.85[/tex]

Generally the probability that a randomly selected ENC that was found to be defective will be made by Alice is

[tex]P(A | D) = \frac{P(A) * p}{P(D)}[/tex]

Here

[tex]P(D)[/tex] is the probability that a randomly selected ENC will be defective and this is mathematically represented as

[tex]P(D) = P(A) * p + P(B) * q + P(C) * r[/tex]

=> [tex]P(D) = 085 * 0.025 + 0.10 * 0.040 + 0.05 * 0.06[/tex]

=> [tex]P(D) = 0.02825 [/tex]

So

[tex]P(A | D) = \frac{ 0.85 * 0.025 }{0.02825}[/tex]

=> [tex]P(A | D) = 0.7522 [/tex]