Question

3. Mr. Jones became seriously ill from ingesting defectively manufactured tablets of Vitamin B12. He intends to file a lawsuit against the most likely manufacturer of the tablets. After a brief investigation, he finds that 35 percent of the B-12 sold in this country is manufactured by Leland Pharmaceuticals, and 65 percent is manufactured by Oscar Pharmaceuticals.Of the B12 manufactured by Leland, 25% percent is sold on the East Coast and 75 percent on the West Coast, while 35 percent of Oscar’s B-12 is sold on the East Coast and 65 percent on the West Coast. Furthermore, Mr. Jones recalls that he purchased his B-12 on the East Coast.

Answer 1

X= leland manufactured the tablet

Y= oscar manufactured the tablet

Z= the tablet is bought from east coast

W = tablet is bought from west coast

given,P(X) =0.35 ,P(Y) =0.65 , P(Z | X) = 0.25 , P(W|X) = 0.75 , P(Z|Y) = 0.35 , P(W|Y) = 0.65

Probabality that X manufactured the tablet provided it was bought from east coast =( P(x manufactured the tablet and it was sold on east coast)) / ( P( the tablet is bought from east coast)

= ( 0.35 * 0.25) / ( 0.35 * 0.25 + 0.65 * 0.35 ) = 0.0875 /0.315 = 0.2777

Probability that Y manufactured the tablet provided it was bought from east coast = 1 - 0.2777 = 0.7223

it is more likely that company Y (oscar) manufactured the tablet provided that it was bought from east coast

so Mr JONES should sue OSCAR pharmaceuticals.