4. (10 points) Frodo and Sam are attempting to sneak into Mordor, and are trying to decide whether to go through tunnels or over a mountain pass. Sam estimates that the probability of danger in the tunnels is 0.3, but the probability of danger in the mountain pass is 0.6. As they approach the tunnels, Frodo draws his magic sword Sting, because he knows that in the presence of danger, Sting glows with probability 0.8; when it is safe, Sting glows with probability 0.1. When he draws the sword, he sees that it is glowing. After a quick calculation, Frodo estimates the probability of danger in the tunnels to be 0.77, and decides to turn back. In the above analysis, what role do each of the following numbers play? (Choose from \"posterior probability\