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?

Answer 1

To determine the complement of the event described, let's first identify which pins were knocked down by the rolls.

You knocked down the following pins:

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

Combining these, the pins that were knocked down are:

• Knocking down pins: {1, 4, 5, 7, 8, 9}

Since in bowling there are 10 pins total, which are typically numbered from 1 to 10, we know the total set of pins is: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The complement of the event (which is knocking down the pins in this scenario) is the set of pins that were not knocked down. To find this, we can subtract the knocked down pins from the total set of pins:

Total pins: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Knocked down pins: {1, 4, 5, 7, 8, 9}

Therefore, the pins that were not knocked down (the complement) can be found as follows: Total pins - Knocked down pins = {2, 3, 6, 10}

Thus, the complement of the event, which represents the set of pins that remain standing, is: {2, 3, 6, 10}.