Question: a company A manufactures 80% of electrocardiograms, the company B manufactures 15% and the Company C 5%. The electrocardiograms manufactured by Company A has a failure rate of 4%, those of the company B rate is 5%, while it is 8% for those manufactured by the company C.

(a) randomly selects an electrocardiogram. What is the probability that it comes from the company A?

(b) were selected randomly electrocardiography and was found to be defective. Find the probability that it comes from Company A.

(c) randomly selects an electrocardiogram. Find the probability that it comes from Company A and it is defective.

(d) randomly selects an electrocardiogram. Find the probability that it comes from Company A and it is not defective.

My try is : D: defective, D': not defective, P(A) = 0.8, P(B) = 0.15, P(C) = 0.08 and P(D|A) = 0.04, P(D|B) = 0.05, P(D|C) = 0.08

(a) P(A|D) = (P(D|A) * P(A)) / (P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C))

. . . . .= (0.8*0.04) / (0.8*0.04 + 0.15*0.05 + 0.05*0.08) = 64/87 = 0.74

(b) P(A|D) = (P(D|A) * P(A)) / (P(D|A)' * P(A) + P(D|B)' * P(B) + P(D|C)' * P(C))

. . . . .= (0.8*0.04) / (0.8*0.04 + 0.15*0.95 + 0.05*0.92) = 64/44 = 0.1451

(c) ?

(d) P(A|D) = 1 - (P(A|D))' = 1 - 0.1451

Please any help is welcome

Thank you for your comprehension