2. A digital transmission channel is a stream of binary digits, 0s and 1s, used to broadcast information from one source to one or many destinations. Such channels are noisy, meaning that any meaningful pattern of 0s and 1s comes mixed with random bits. Pure noise is modeled as white noise, which is a sequence of random bits (0s and 1s), independent and all with probability 1/2 (a sequence of Bernoulli trials). Thus, for example, any single 3-bit sequence (an octet) has probability 1 2 1 2 1 2 = 1 8 . In the following we are receiving white noise.

2.1) We received 3 bits, two of them being 1s. What is the probability that the remaining one is a 0?

2.2) We received 3 bits, the first two being 1s. What is the probability that the third will be a 0?