1. Let ? be a space of results and B one happening such that probability of B > 0 (P(B) > 0). Prove that for any happening A, we have:
P(A|B) + P(?\ A|B) = 1
2. In a Phone Central, we observe, every minute, if certain phone line is or is not occupied. In this way, it has been told that the probability of certain line is occupied in certain moment, if in the last minute was free, is 30% and the probability of certain line is free if in the last minute was occupied is 25%.
2.1 Identify the space of results of an observation of 2 consecutive minutes.
2.2 Identify the probability of certain line be free if in the last minute was free.
2.3 If certain line is occupied in a certain moment, what is the probability of that line be free in the next minute? Explain.