Suppose a builder, named Bob, wants to hammer in 20 nails into a piece of wood. Bob is very strong and can hammer down a nail in a single blow if he hits the nail square on its head. But Bob is also a little near-sighted and, in any given swing of his hammer, he only hits any given nail square on its head with probability p = 1/3 and misses it completely with probability 1 − p. Derive a bound on the probability that it takes Bob more than 120 swings to hammer down all 20 nails.