There are three factories responsible for producing certain components that are distributed to other companies to be used. All factories produce defective components that occur at random. Factory A is used 60% of the time, factory B 25% of the time and C 15% of the time. Factory A produces components with a 15% defective rate, B at a rate of 5%, and C at 10%. You receive a shipment from one of the factories, and you examine one component after the other. It takes 18 components TO find the first defective one.

Find the probability the shipment came from factory C. Round intermediate steps to four decimal places.