Suppose that three floors of a dungeon each contain rooms with swords, gold, and wumpuses (wumpi?). No rooms are empty, and each room contains only one item. No room can contain both gold and a wumpus, for example. The distribution of these floors are as follows:
Floor 1: 11 rooms total. 2 have swords, 3 have gold, and 6 have wumpuses.
Floor 2: 9 rooms total. 4 have swords, 2 have gold, and 3 have wumpuses.
Floor 3: 10 rooms total. 3 have swords, 4 have gold, and 3 have wumpuses.
An agent randomly picks a floor to appear on, paying no attention whatsoever to the number of rooms on each floor.
(a) What is the probability that the agent will appear on Floor 1? (6 points)
Now that the agent has chosen a floor, the agent now randomly picks a room to appear in within that floor. On doing so, it finds a sword in the room it appears in.
(b) With this additional information, now what is the probability that the agent is on Floor 1