Question

13. (Bayes' Theorem). Company makes product at three factories. From past records, they know the proportion of output from each factory and the percentage of defects that come from each factory. The information is shown in the table. Defects (%) L Output (%) 20 15 65 A quality control engineer selects a ski binding at random. Let B1, B2, and Bs represent the event that the binding comes from factory 1, factory 2, or factory 3, respectively, and let A represent the event that the binding has a defect. a. Construct a tree diagram b. Determine P ( B A) and interpret.

Answer 1

Given that A is the event that the product is defective and Bi B2 B3 is the event that dhe ski binding comes from factory 1.23 respect vely a) The tree diagram information given can be constructed from the in the table as follows

0.02 Defectiu PCA BIJA : .2 l PCBI) = 0.2 - Not defectin 0.03 Defectiu PLAIB2) A P(B2) = 0.15 2 PCB3)=0.65 - Not defectiu ool defection 3 P(A/B3) A 33 Not defective (b) To find P(B2/A) from the tree diagram we see that PCB2/A) = PCB2) PCA/B2) PCB,) PCA/RI) + PCB) PCA482) +PCB3) PCA/B3) 0.15*0,03 CO 2X0.02) +C0119x0,03) +(0.65X0.01)

&: 0.0045 0.004 +0.0045 +0,0065 R 0.0045 01015 30.3 P (B2/A) = 0.3 If a ski binding is drawn at random and It is found to be defective (A) then P (B21A) represents the probability that the sia binding is from factory - 2 which is 013 or 30%