Question

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?

Option #1: {3,4,6,9}


Option #2: {2,3,6,10}


Option #3: {1,4,5,7,8,9}


(1 point)
Option #
is a subset that is a complement of the event.

Answer 1

To determine which option represents a subset that is a complement of the event (knocking down the pins you have knocked down), we first identify which pins have been knocked down.

From your description:
- You knocked down pins 9, 5, 7, and 1 in the first roll.
- You knocked down pins 4 and 8 in the second roll.

The total pins knocked down are:
1, 4, 5, 7, 8, 9.

The event consists of these knocked down pins:

**Knocked down pins:** {1, 4, 5, 7, 8, 9}

Now, the total pins in bowling are:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

The complement of the event (the pins that were not knocked down) would be:

**Remaining pins (complement):** {2, 3, 6, 10}.

Now let's analyze the options:

- **Option #1:** {3, 4, 6, 9}
- This includes pins 4 and 9, which were knocked down.

- **Option #2:** {2, 3, 6, 10}
- This includes only pins that were not knocked down, making it a valid complement of the event.

- **Option #3:** {1, 4, 5, 7, 8, 9}
- This includes all knocked down pins.

Thus, the only option that is a subset that is a complement of the event is:

**Option #2: {2, 3, 6, 10}**