Answer:
a) 1.682%
b.) 99.98779
Step-by-step explanation:
work below
all you really need to know for this question is law of total probability and the conditional probability formula
Answer:
(a): 1.682 %
(b): 99.98779 %
Step-by-step explanation:
Using the shorthands for the event “item classified as defective” C and “item is defective” D
(a): [tex]P(C) = P(C \cap D) + P(C \cap \overline{D}) = P(D)\cdot P(C | D) + (1-P(D))\cdot P(C | \overline{D}) = 0.012\times 0.99 + 0.988\times 0.005[/tex]
(b): [tex]P(\overline{D}|\overline{C}) = \frac{P(\overline{D} \cap \overline{C})}{P(\overline{C})} = \frac{P(\overline{D})}{P(\overline{C})}\times P(\overline{C} | \overline{D}) = \frac{1 - P(D)}{1 - P(C)}\times (1-P(C | \overline{D})) = \frac{0.988}{0.98318}\times 0.995[/tex]
