Answer:
The probability is [tex]P(C | I) = 0.025[/tex]
Step-by-step explanation:
From the question we are told that
The proportion analyzed by Amir is P(A) = 0.55
The proportion analyzed by Betty is P(B) = 0.30
The proportion analyzed by Carlos is P(C) = 0.15
The inaccuracy by Amir is p = 0.6% = 0.006
The inaccuracy by Betty is b = 0.4% = 0.004
The inaccuracy by Carlos is c = 0.1% = 0.001
Generally the probability of inaccurate analysis is mathematically represented as
[tex]P(I) = P(A) * p + P(B) * b + P(C) * c[/tex]
=> [tex]P(I) = 0.55 * 0.006 + 0.30 * 0.004 + 0.15 * 0.001 [/tex]
=> [tex]P(I) = 0.006 [/tex]
Generally the probability that an inaccurate analysis, detected at final verification, was conducted by Carlos is mathematically represented as
[tex]P(C | I ) = \frac{P(C) * c}{P(I)}[/tex]
=> [tex]P(C | I) = \frac{ 0.15 * 0.001}{ 0.006}[/tex]
=> [tex]P(C | I) = 0.025[/tex]
