Final answer:
The sample space S is the set of whole numbers starting at one and less than twenty. Event A is the set of even numbers in the sample space, and event B is the set of numbers greater than thirteen. The probability of event A is 9/19 and the probability of event A AND B is 3/19.
Step-by-step explanation:
The sample space S can be represented as the set of whole numbers starting at one and less than twenty. So, S = {1, 2, 3, ..., 19}.
Event A can be defined as the set of even numbers in the sample space, which is A = {2, 4, 6, ..., 18}.
Event B can be defined as the set of numbers greater than thirteen in the sample space, which is B = {14, 15, 16, ..., 19}.
The intersection of events A and B (A AND B) is the set of numbers that are both even and greater than thirteen. In this case, A AND B = {14, 16, 18}.
To find the probability of an event, we use the formula P(A) = number of outcomes in A / total number of outcomes. Since the sample space S has 19 elements, the probability of event A (P(A)) is 9 / 19. The probability of event A AND B (P(A AND B)) is 3 / 19.