A furniture manufacturer sells three types of products: chairs, tables, and beds

Question

A furniture manufacturer sells three types of products: chairs, tables, and beds. Chairs constitute 45% of the company's sales, tables constitute 35% of the sales, and beds constitute the rest. Of the company's chairs, 8% are defective and have to be returned to the shop for minor repairs, whereas the percentage of such defective items for tables and beds are 4% and 5% respectively. A quality control manager just inspected an item and the item was not defective. What is the probability that this item was a chair? Round your result to 2 significant places after the decimal (For example, 0.86732 should be entered as 0.87).

Explanation / Answer

P(not defective)=P(chair & not defecitve+table & not defecitve+bed & not defecitve)

=0.45*(1-0.08)+0.35*(1-0.04)+0.2*(1-0.05)=0.94

hence P(chair|not defective) =0.45*(1-0.08)/0.94 = 0.44

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