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 defective item has just been returned to the shop for minor repairs. 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(defective)=P(chair and defective+table and defective+bed and defective)

=0.45*0.08+0.35*0.04+0.2*0.05=0.06

hence  probability that this item was a chair given defective

=P(chair and defective)/P(defective) =0.45*0.08/0.06=0.6

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