Question

2-148. An inspector working for a manufacturing company has a 98% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defec- tive. The company has evidence that 1% of the .ems its line produces are nonconforming. (a) What is the probability that an item selected for inspection is classified as defective? b) If an item selected at random is classified as nondefective, what is the probability that it is indeed good?

Answer 1

TOPIC:Theorem of total probability, Bayes' theorem.

2-148) S Define the events G ! The selected item is good. as defective. and D classified : The item is . Given that, PC The item is | The item is I classified as I not good defective 2 100 sy P (A1GC) = 0.98 .. Now, =) P (299)=1-P (AIG) = 0.02. also, (The item is I The item is-0.005 classified as good (in decimals) I good defective => P (AIG) = 0.005. = P(ala) = 1-P (21G) = 0.995.

Now, I of an item is non-conforsming] =0.01. > P I of an item is not good] = o.o. =) P (a) 20.01. so P(a) = 1-P (66) = 1-0.01 = 0.99. a) we need => pl of classifying an item as defective = P(2), T Theorem 017 = P(219) P (G) + P(2149).p(QC). total proobability o. 98xo.ol. 0.0058o .99+ - 10.01475) (ons) by we need, EXP [The item is 1 It is classified Lindeed good as non-defective - & (ala). - P(a). P (2016) P(G). P (2016) +P (6). P(219) Bayes! - theorems 0.99 x 0.995 0.99 X 0.995 + 0.01 0.02 - 0.999797 339/26 (ên. (Ansl (in 6 decimals)