An item is manufactured by three plants ๐1, ๐2 and ๐3. The market
share of the plants are 10%, 70%, and 20% respectively. The defective
rates of the products from the three plants are ๐1 = 6%, ๐2 = 2.5%, and
๐3 = 3.5%.
What is the probability that plant ๐2 did not manufacture a randomly
purchased item given that the item is defective?