Final answer:
The probability of selecting an even number (Event A) from the sample space is 7/15. Event B comprises numbers greater than 13, which are {14, 15}, and the intersection of A and B is only the number 14, leading to a probability of P(A AND B) which is 1/15.
Step-by-step explanation:
Given the sample space S = {1, 2, 3, 4, ..., 15}, a single number is selected at random. The events are described as follows:
- Event A: The selected number is even.
- Event B: The selected number is greater than 13.
To find Event A, we list all the even numbers in the sample space: A = {2, 4, 6, 8, 10, 12, 14}.
To find Event B, we list all the numbers greater than 13: B = {14, 15}.
To find the probability of event A, P(A), we calculate:
P(A) = number of outcomes in A / number of outcomes in S. There are 7 even numbers and 15 total numbers, so P(A) = 7/15.
The intersection of events A and B, A AND B, is the set of numbers that are both even and greater than 13: A AND B = {14}.
Therefore, the probability of A AND B, P(A AND B), is the probability of getting a 14 when a number is selected at random from S, which is P(A AND B) = 1/15.