Question 1.1 [5 points] - Some Intuition about Hash Collisions The details of how different hash functions work, including how they are implemented and their statistical properties, are mostly beyond the scope of this class. However, a feature common to all hash functions is collisions. When dealing with hashing, it's helpful to have some intuition about the frequency of collisions. Recall that a collision occurs whenever for two distinct elements a and b and a hash function h(x),h(a)=h(b). Assume you have a hash function (the actual process by which it operates is unknown) with the following properties: - The outputs (hash values) are of size 8 bits (there are 256 possible hash values/buckets). - The hash function distributes its outputs evenly across the entire output range (this property is very desirable in hash functions and is called uniformity). What is the probability of having at least one collision if we are hashing 5 inputs? Give your answer as a numerical value (not an equation) but show some work/reasoning. A simple numerical answer with no reasoning will not count for full points. What about for 10 inputs? 20 inputs? 50 inputs