Mutually Exclusive Events Practice Test

A hospital records one patient’s status at a randomly chosen time today. Let event $A$ be “the patient is in the emergency department” and event $B$ be “the patient is in the operating room.” Hospital policy states a patient can be in only one location at a time. Are the two events mutually exclusive?

A number is randomly selected from the set ${1,2,3,4,5,6,7,8,9,10}$. Let event $A$ be “the number is prime” and event $B$ be “the number is even.” The number 2 is both prime and even, so the events can occur together. Are the two events mutually exclusive?