Question

A factory has two production lines A and B, production line A works 7 days a week, production line B works only 5 days a week. Production line A produces 5000 items each day where 91% of the produced items are high quality and the rest are of medium quality. Production line B produces 3500 items each day where 62% of the produced items are high quality, 15% medium quality, and the rest are of low quality. All items produced after working for many weeks are accumulated in a warehouse. If an item is tested and found to be of medium quality, what is the probability that it was produced by production line A. [The answer should be a number rounded to five decimal places, don't use symbols such as %]

Answer 1

Solution An item is tested and found to be medium qaboy probability that it was produced by proderties line as - A- proderet choosen from linen. B - product choosen from linee £ = pro babruty of medium quality PELA) - 1-0.91 PLEIB) = 18% 2 = 0.09 0-15 Are rage total items produced in linea ina weebr : 5000*= 3500 0. lineB2- 3500 x 5 = 172500 Tual itens prodeled - 35000 +17670 = 521500 PA) = 350 00 17500 P(B) - 52,500 52,500 = 0 3333 0.6667 > PC ALE) - P(PLA). PLM) '( F/A). PCA) + P(B1B). Þ(B) 0.09) (0.6667 0.060003 0.109998 [60.09) (96663)] + Co. 0.15* 013333] 0:50549 (Rounded to 5 deemal places probability that the item prodeeced by production line a 0.5u549. # 005