At the station there are three payphones which accept 20p pieces. One never works, another always works, while the third works with probability 1/2. On my way to the metropolis for the day, I wish to...

Extracted text: At the station there are three payphones which accept 20p pieces. One never works, another always works, while the third works with probability 1/2. On my way to the metropolis for the day, I wish to identify the reliable phone, so that I can use it on my return. The station is empty and 1 have just three 20p pieces. I try one phone and it does not work. I try another twice in succession and it works both times. What is the probability that this second phone is the reliable one?