Question

In bowling, there are 10 pins that stand in a triangular shape. The idea is to knock down all of the pins. A frame consists of two rolls (if you don't knock down all 10 pins in the first roll).



On your first roll, you knock down pins 2, 5, 7, and 8; in the second roll, you knock down pins 9 and 10.



Which of the following is a subset that is a complement to the event?

Answer 1

In bowling, to identify the complement of the set of knocked down pins, we first need to know the set of all possible pins and then determine which pins remain standing after the rolls.

The total set of pins is:
\[
\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
\]

From your rolls:
- In the first roll, you knocked down pins 2, 5, 7, and 8.
- In the second roll, you knocked down pins 9 and 10.

So, the total pins knocked down are:
\[
\{2, 5, 7, 8, 9, 10\}
\]

Now, we can find the complement, which is the set of pins that are still standing. To find this, we subtract the knocked down pins from the total set of pins:

Standing pins:
- Pin 1 (not knocked down)
- Pin 3 (not knocked down)
- Pin 4 (not knocked down)
- Pin 6 (not knocked down)

Thus, the complement set (the pins that remain standing) is:
\[
\{1, 3, 4, 6\}
\]

This subset represents the event of the remaining standing pins after your rolls.