pr.probability – Probability problem – MathOverflow

A company offers three different categories of roofing ties: Stone, Clay, and Ceramic. They guarantee the highest customer satisfaction, and claim that every batch of tiles produced is tested for its longevity. For every batch of 70 Stone tiles, 48 pass, 5 break, and the rest are sent to be refurbished. For every batch of 55 Clay tiles, 25 pass, 11 fail, and the rest are refurbished. And for every 60 Ceramic tiles, 43 pass, 7 fail, and the rest are refurbished. The sales record of the company shows that 47%, 22%, and 31% of their orders are for Stone, Clay, and Ceramic tiles respectively. A tile was randomly selected from an order and separately tested four times, two of which it failed. What is the probability that the tile was made of ceramic?