Answer: The simple predicate in the sentence is "has been waiting".
Explanation: A simple predicate is the verb or verb phrase of a sentence. It does not include any of the words that modify this verb or verb phrase. The simple predicate of a sentence indicates what the subject is, does or feels. In the sentence provided ("My mother has been waiting all morning for the plumber to arrive"), the simple predicate is "has been waiting" because it is the verb that shows what the subject, "My mother", has been doing.
