To find the complement of the event of the numbers you drew (which are 3, 12, and 1), we need to determine the set of numbers that are not in the event.
The event consists of the numbers you drew: {1, 3, 12}.
The complete set of possible numbers (the universal set) is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}.
To find the complement, we remove the numbers you drew from the universal set:
Universal set: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} Numbers drawn: {1, 3, 12}
The complement will consist of the remaining numbers: {2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}.
Now let's look at the options provided:
Option #1: {empty set} Option #2: {1,3,12} Option #3: {2,4,5,6,7,8,9,10,11,13,14,15}
The correct answer is Option #3: {2,4,5,6,7,8,9,10,11,13,14,15}, as it describes the complement of the event of the numbers you drew.