Question

Three machines called A, B and C, produce 43%, 26% and 31% of the total production of a company, respectively. Furthermore, it has been detected that 8%, 2% and 1.6% of the product manufactured by these machines is defective. a) What is the probability that a product is not defective? b) A product is selected at random and found to be defective, what is the probability that it was manufactured on machine B?

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a)
P(A no defectuoso) = (1-8%)(43%) = 0,3956
P(B no defectuoso) = (1-2%)(26%) = 0,2548
P(C no defectuoso) = (1-1,6%0)(31%) = 0,30504
P(no defectuoso) = 0,3956 + 0,2548 + 0,30504
= 0,95544
b)
P(B dado defectuoso) = P(B y defectuoso)/P(defectuoso)
= (2% x 26%)/ (1-0,95544)
= 0,1166965889

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