Question

In a laboratory, 3 technicians are analyzing the active ingredient in the product vials. Amir, Betty, and Carlos analyze 0.55, 0.30, and 0.15 of the vials, respectively. Inaccurate are 0.6 percent of the analyses conducted by Amir, 0.4 percent of the analyses conducted by Betty, and 1.0 percent of the analyses conducted by Carlos in this study. What is the probability that an inaccurate analysis, detected at final verification, was conducted by Carlos

Answer 1

The probability is
`P(C | I) =  0.025`

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

`P(I) =  P(A) *  p  +  P(B) *  b  +  P(C) *  c`

=>
`P(I) =  0.55 * 0.006  +  0.30  *  0.004  +  0.15  *  0.001`

=>
`P(I) =  0.006`

Generally the probability that an inaccurate analysis, detected at final verification, was conducted by Carlos is mathematically represented as

`P(C | I ) =  (P(C) *  c)/(P(I))`

=>
`P(C | I) =  (   0.15  *  0.001)/( 0.006)`

=>
`P(C | I) =  0.025`