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?

Question

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

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

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

(1 point)

Answer 1

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

From the rolls given:

• In the first roll, you knocked down pins {1, 5, 7, 9}.
• In the second roll, you knocked down pins {4, 8}.

So, the total set of knocked down pins is {1, 4, 5, 7, 8, 9}.

The complement of the knocked down pins would be the pins that were not knocked down. Therefore, the complement set is: {2, 3, 6, 10}.

Now we can evaluate the options:

Option #1: {3,4,6,9} - Contains 4 and 9, which are knocked down. Not a subset of the complement.

Option #2: {2,3,6,10} - All of these pins were not knocked down. This is the complement set.

Option #3: {1,4,5,7,8,9} - All of these pins were knocked down. Not a subset of the complement.

The correct answer is Option #2: {2,3,6,10}.