Question

Please explain by calculation, thank you!

Answer 1

Answer:

correct option is b)0.16%

Step-by-step explanation:

given data

defect rate P(defect ) = 3 % = 0.03

Inspectors catch = 95%  = 0.95

fail nondefective =  5% = 0.05

solution

we get here  P(No Defect)  that is

P(No Defect)  = 1 - P( Defect)   .........1

P(No Defect)  = 1 - 0.03

P(No Defect)  = 0.97

and

P(Pass | Defect)  will be

P(Pass | Defect)  = 1 - Inspectors catch   ...........2

P(Pass | Defect) = 1 - 0.95

P(Pass | Defect)  = 0.05  

and

P(Pass | No Defect) is

P(Pass | No Defect) = 1 - fail non defective    ..............3

P(Pass | No Defect) = 1 - 0.05

P(Pass | No Defect) =  0.95

so now we apply here Baye's theorem

so

P(Defective | Pass)  is

P(Defective | Pass)  = $\frac{0.03*0.05}{(0.03*0.05)+(0.97*0.95)}$  

P(Defective | Pass)  = 0.0016

P(Defective | Pass)  = 0.16 %

so correct option is b)0.16%