Final answer:
Events A and B are mutually exclusive because it is impossible for a student to be born on the 30th of a month and also be born in February, which only has 28 or 29 days.
Step-by-step explanation:
To determine whether the events are mutually exclusive, we need to check if both events can occur at the same time.
Event A: Randomly select a student born on the 30th of a month
Event B: Randomly select a student with a birthday in February
Since February has only 28 or 29 days (in the case of a leap year), it does not have a 30th day. Therefore, no student can be born on the 30th of February, as February does not have this date. In other words, if Event A occurs (a student is selected with a birthday on the 30th), they cannot also have been born in February (Event B), and vice versa.
So, based on the definition that events are mutually exclusive if they cannot occur at the same time (which means the probability of A and B happening together is zero), we can conclude that Events A and B are mutually exclusive, because P(A AND B) = 0.