A bag has 15 numbered tiles inside, numbered 1-15. Without looking, you reach in and pull out one tile at a time, without returning the tile to the bag. The numbers you draw are 3, 12, and 1.

Question

Which of the following options describes the complement of the event of the numbers you drew?
Option #1: {empty set}
Option #2: {1,3, 12}
Option #3:
{2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}
(1 point)
8
Option #
describes the
complement of the event.

Answer 1

The complement of the event of drawing the numbers 3, 12, and 1 refers to all the outcomes that are not part of the event. In this case, the event consists of the numbers you drew.

Since there are 15 tiles numbered from 1 to 15, the complement will include all the numbers that were not drawn.

The numbers drawn are:

• 1
• 3
• 12

The complement, therefore, consists of the numbers:

• 2
• 4
• 5
• 6
• 7
• 8
• 9
• 10
• 11
• 13
• 14
• 15

Thus, the complement of the event you drew (3, 12, 1) is given by:

Option #3: {2, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15}.

So the correct answer is Option #3.