Respuesta :
The fraction of a defective item getting by both inspectors is [tex]\frac{5}{100}[/tex] = [tex]\frac{1}{20}[/tex]
Step-by-step explanation:
Step 1; Assume that the probability of the first inspector missing a defective part is P(A) and the probability of the second inspector missing those that do get past the first inspector is P(B).
Step 2; It is given that P(A) = 0.1, we convert this into a fraction so that the final probability will be a fraction and not a decimal.
P(A) = 0.1 = [tex]\frac{1}{10}[/tex].
It is given that the second inspector misses 5 out of 10 that get past the first inspector, so P(B) = [tex]\frac{5}{10}[/tex].
Step 3; To calculate the probability of both inspectors missing a defective part, we multiply both the probabilities.
P(A and B happening) = P(A) × P(B) = [tex]\frac{1}{10}[/tex] × [tex]\frac{5}{10}[/tex] = [tex]\frac{5}{100}[/tex] = [tex]\frac{1}{20}[/tex] = 0.05%. So there is a 0.05% chance of both inspectors missing a defective part.
