An analog to digital (A/D) converter generates 3-bit digital words correspond- ing to eight levels of the input signal (0, 1, ..., 7) with the following prob- abilities: Pr[0] = Pr[1] = Pr[6] = Pr[7] = 1/16, Pr[2] = Pr[5] = 1/8, and Pr[3] = Pr[4] = 1/4. 1. Find the probability that the input has a value > 5 given that the first hit of t he output is a 1. 2. Find the probability that the first bit is a 1 given that the input value is greater than 5. 3. What is the probability of a binary 1? 4. Determine the probability of a binary 0.