Question
A bag has 12 numbered marbles inside, numbered 1–12. Without looking, you reach in and pull out one marble at a time, without returning the marble to the bag. The numbers you draw are 2, 5, and 11. Which of the following options describes the complement of the event of the numbers you drew? Option #1: {empty set} Option #2: {2,5,11} Option #3: {1,3,4,6,7,8,9,10,12}
Answers
GPT-4o mini
To determine the complement of the event of drawing the numbers 2, 5, and 11 from the bag, we need to identify all the numbers in the bag and then find those that were not drawn.
The bag contains marbles numbered from 1 to 12:
- Full set of marbles: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
The numbers drawn are: {2, 5, 11}
The complement of the event of drawing the numbers {2, 5, 11} is the set of numbers that are **not** drawn.
Thus, we need to find the numbers from the full set that do not include 2, 5, and 11:
- Remaining marbles: {1, 3, 4, 6, 7, 8, 9, 10, 12}
Now, let's look at the provided options:
- Option #1: {empty set} – This is not correct as there are numbers that were not drawn.
- Option #2: {2, 5, 11} – This represents the event of the numbers you drew, not the complement.
- Option #3: {1, 3, 4, 6, 7, 8, 9, 10, 12} – This represents all the numbers not drawn, which aligns with the complement of the event.
Therefore, the correct answer is **Option #3: {1, 3, 4, 6, 7, 8, 9, 10, 12}.**
The bag contains marbles numbered from 1 to 12:
- Full set of marbles: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
The numbers drawn are: {2, 5, 11}
The complement of the event of drawing the numbers {2, 5, 11} is the set of numbers that are **not** drawn.
Thus, we need to find the numbers from the full set that do not include 2, 5, and 11:
- Remaining marbles: {1, 3, 4, 6, 7, 8, 9, 10, 12}
Now, let's look at the provided options:
- Option #1: {empty set} – This is not correct as there are numbers that were not drawn.
- Option #2: {2, 5, 11} – This represents the event of the numbers you drew, not the complement.
- Option #3: {1, 3, 4, 6, 7, 8, 9, 10, 12} – This represents all the numbers not drawn, which aligns with the complement of the event.
Therefore, the correct answer is **Option #3: {1, 3, 4, 6, 7, 8, 9, 10, 12}.**