Collisions in Hash Tables (a) (10 pts) Consider a hash table with m slots that uses chaining for collision resolution. The table is initially empty. What is the probability that, after three keys are inserted, there is a chain of size 3? Show your work! (b) (10 pts) Consider a hash table with m slots that uses open addressing with linear probing. The table is initially empty. A key k is inserted into the table, followed by key k2. What is the probability that inserting key ks requires three probes? Show your work