Question

Circuits. Quality control. During a final inspection of circuits, circuits that are not fully functional should be sorted out. It is known that on average 20%
the generated circuits are not fully functional. When testing, 95% of these circuits are sorted out, but also 1% of the perfect ones.
1. What is the probability that a circuit that has not been sorted out is fully functional?
2. What is the probability of a rejected circuit being faultless?

Answer 1

het I denotes the event that randomly selected circuit is fully functional and B denotes the event that randomly selected circuit is sorted out the generated not fully are I 20% of circuits functional. ..P(A²) = 0.20 When the resting, 95% of that are fully functional circuits not sorred out. are :P(BIA) = 0.95. are When resting, 1 % of the circuits that fully functional

Req sorted out. . PIBIA ) = 0.01 probability P(Al B²) Plan Be P(Be)

PCB'IA) PLA 1) 1- PIB) {,- P(BIA) } P(A) I-PIB) = [ Now, PIB) PIBIA ) PIA) P PIBIA e PLA

+ 2 PL BIA) {1-P1A²)] PI BIA") .P(A²) + - 0.01x (1-0.20) 0.95 x 0.20 O. I g 8

2 that for We know any E and F events PLEIF) + PlEllF) = 1 : PIBIA) Pl B²1A)=1 P (BIA)=1- P(BIA) 11 -0.01 ) x (1-0.20) 0.198 [ PLA)=1-PLA) 2 1 - 0 20 0.80. 0 792 0.802 0 9 8 75.