Question: An underwriter of home insurance policies studies the problem of home fires resulting from wood-burning furnaces. Of all the homes having such furnaces, 30% own a type 1 furnace, 25% a type 2 furnace, 15% a type 3, and 30% other types. Over three years 5% of type 1 furnaces, 3% of type 2, 2% of type 3, and 4% of other types have resulted in fires. If fire occurs in a particular home, what is the probability of that a type 1 furnace is in the home?