Question

In bowling, there are 10 pins that stand in a triangular shape. The idea is to knock down all the pins. A frame consists of two rolls (if you don't knock all 10 pins down in the first roll). On your first roll, you knock down pins 9, 5, 7, and 1; in the second roll, you knock down pins 4 and 8. Which of the following options is a subset that is a complement of the event?(7 points)
Responses

{3,4,6,9}
{3,4,6,9}

{2,3,6,10}
{2,3,6,10}

{1,4,5,7,8,9}
{1,4,5,7,8,9}

{1,2,3,4,5,6,7,8,9,10}

Answer 1

In bowling, the set of all pins is represented by {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

From your rolls, you knocked down the following pins:

- First roll: 1, 5, 7, 9
- Second roll: 4, 8

So, the pins that were knocked down in total are {1, 4, 5, 7, 8, 9}.

The remaining pins that are still standing (not knocked down) are:

{2, 3, 6, 10}

Now, a complement of the event (knocking down the pins mentioned) must include the pins that were not knocked down.

Let's analyze the options based on this:

1. {3, 4, 6, 9} - Contains pin 4 and 9 (which were knocked down), so it is not a complement.
2. {2, 3, 6, 10} - Contains all the pins that were not knocked down. This is the complement of the event.
3. {1, 4, 5, 7, 8, 9} - This is the set of knocked down pins, so it is not a complement.
4. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} - This is the universal set of all pins.

The correct option that represents the complement of the event is:

**{2, 3, 6, 10}**