"Life is a paradox, you're damned if you do and damned if you don't"

This is one of my Fav paradoxes. A lil girl from Australia sent it to me last year. Read on.... According to the principle of indifference, if we have no good reason for preferring one truth value over another as regards a particular proposition, we should assign a probability of 1/2 to that proposition. This principle is open to many forms of abuse, the most popular illustration of this being the life on Mars paradox, which is presented below in the form of a dialogue between A and B. A: What is the chance of there being some form of life on Mars? B: I have no good evidence for or against, so I will answer 1/2. A: OK. Now what's the chance of no animal life on Mars? B: Again, I must answer 1/2. A: And the chance of no non-animal life on Mars? B: Again, 1/2. A: So the chance of no life (ie. no animal life and no non-animal life) on Mars = 1/2 x 1/2 = 1/4? B: Well, yes, I suppose so. A: But then the probability of some life on Mars must be 1 - 1/4 i.e. 3/4? B: Wel...that seems to follow, all right. A: You agree then that 1/2 = 3/4? B: Now hold on a minute! What went wrong?