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 is a subset that is a complement of the event of knocking down certain pins, we first need to identify which pins were knocked down.

From the description:

• In the first roll, the knocked down pins are: 1, 5, 7, and 9.
• In the second roll, the knocked down pins are: 4 and 8.

Combining the pins knocked down from both rolls, we get the set of knocked down pins: {1, 4, 5, 7, 8, 9}.

Now we identify which pins remain standing (not knocked down). The full set of pins is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The pins that remain standing are those that are not in the knocked down set:

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

Remaining pins (complement of the knocked down pins):

• {2, 3, 6, 10}

Now we will analyze the options to see which one is a subset of the remaining pins:

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

• This option includes pins: 4 and 9 which are knocked down. Therefore, it is not a subset of the standing pins.

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

• This option includes all pins that remain standing: 2, 3, 6, and 10. So it is indeed a subset of the standing pins.

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

• This option includes pins that were knocked down, hence it is not a subset of the standing pins.

Thus, the only option that is a subset that is a complement of the event (the pins that remain standing) is:

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