Exercise 2. Probabilities [50 points] Let s be a binary string of size 4 bits. Compute the following: How many possible strings of length 4 are there? What is the probability that the first bit of s is equal to 0? How about the probability of the second bit of s is equal to 0? How about the last bit? What is the probability that the last two bits are all 1's ? What is the probability that the first 2 bits are equal to the last 2 bits? Now, consider the more general case of a binary string s of size n bits. Compute the following: How many possible strings of length n are there? What is the probability that the first bit of s is equal to 0? What is the probability that the first bit and the last bit of s are equal? What is the probability that s begins with "000" ? What is the probability that the first half bits are equal to the last half bits? (assume that the n is even)