#
Question

Alice passes through four traffic lights on her way to work, and each light is equally likely to be green or red, independent of the others. Let X be the number of red lights that Alice encounters. Let A be the event that the first light is red.

What is the PMF of X given A, i.e., PX|A(x)?

What is the mean of X given A, i.e., E[X|A]?