Question

You have been trapped in a building with 3 hallways, and each of them can lead to your freedom.

Unfortunately for you, each of these 3 hallways has 2 doors. Each of the six doors could be

locked or unlocked independent of any other door. To be able to escape to

freedom through a particular hallway, you require that both the doors in that hallway are

unlocked.

The doors in hallway 1 is independently locked with probability 1/2

The doors in hallway 2 is independently locked with probability 1/3

The doors in hallway 3 is independently locked with probability 1/4

What is the probability that hallway 1 was open (in essence, both doors in hallway A were

unlocked) given that you managed to escape to freedom? Assume that if a hallway is closed you can go back and try another one.

Answer 1

In this context

Probabiliy for a Hallway = 1/3

Probability for hallway to be open = 0.5

Probability for Escape = P(hallway open and door 1 open and door 2 open)

=