2. We have 2 types of binary sources. Each source outputs one bit, i.e. '0' or '1', independently at each time instant: for a source of type A, the probabilities are P(0) = 0.5, P(1) = 0.5 whereas for a type B source, the probabilities are P(0) = 0.9, P(1) = 0.1. Someone gives us a box containing 5 unlabelled, identical-looking sources, 4 of which are of type A and 1 of type B. We choose one of the 5 sources at random and observe its output at 4 time instants. Suppose that the four observed bits are all O's, what is the probability that we chose a type A source