Question

Problem 03 A set of 500 machine parts are inspected before they are shipped. I denotes a machine part that is improperly assembled. D denotes that the machine part was assembled with one or more defective components. The distribution of the 500 machine parts among the various categories as... 20 5 10 465 S Determine the probability that a randomly selected machine part with be observed to be incorrectly assembled if the inspector knows that there is a defective part used in the production. Determine the probability that a randomly selected machine component will be observed to be incorrectly assembled if the inspector knows that the all of the components in the part are functional.

Answer 1

② pl Probs that incomectly assembled functional) - part Assumption : - given that all parts are funcion parts apost from defectives functional I from defectives ones are # of functional pails = 500 - = 502-15 sony (1075) M - N(F) = 485 P(I/E) = P(IRF) , where D P(F) = purb. of part being functional but assembled inconectly. Plas pub.of part being functione a random selection is made P(Inf) = N(INF) o N(Total parts) = P(F) = # of functional pents Total # of parts Shaded portion are functional parts 485 500 20 204 : Palermo su 48- 485

Soin. . pants Given, Total # of machines - 500 I- machine part is improperly assembled D- machie part with to 2 or defective (Ind) =10 S=465 I 20 Bos INDE 10 Esno Incomeatly P(D) {p(y) in prob. of (a) - pl part in assembled given that I there is defective part used =P(ID) PE thing a conditional perbolikty law. . where P (IND) is prob- of getting defective part assembled inconectly. Plo) i prob- of getting defective part & P(IND) - # of (defective part beingen) Total of of pants - - - w the parts P(3) = T #of defective parts Total #of parts , P/IND) = 10 ; Plo)= 18 - P(ID) - - 5110 10 STO Amer 15 12