Consider an open-address hash table with uniform hashing. Give upper bounds on the expected number of probes in an unsuccessful search and on the expected number of problems in a successful search when the load factor is $3/4$ and when it is $7/8$.
Those come directly from our formulas:
What I find interesting, is that successful searches are dramatically less probes than unsuccessful searches. This implies that with uniform hashing the load factor can be pretty high if we're using the hash looking things up as opposed to checking if an element exists.