In bowling, there are 10 pins that stand in a triangular shape. The goal is to knock down all the pins. You have two chances to roll the ball and knock down pins, if you don't knock all of them down on the first roll. Suppose on your first roll, you knock down the 2,3,5 and 10 pins. On your second roll you knock down the 6 and 7 pins. The pins are numbered as shown below.

Question

In bowling, there are 10 pins that stand in a triangular shape. The goal is to knock down all the pins. You have two chances to roll the ball and knock down pins, if you don't knock all of them down on the first roll. Suppose on your first roll, you knock down the 2,3,5 and 10 pins. On your second roll you knock down the 6 and 7 pins. The pins are numbered as shown below.
Which of the following options is a subset that is a complement of the event? Option #1: {2,3,5,6, 7,10} Option # 2: {6,7} Option # 3: {1,4,8,9} Option #4: {2,3,5,10}
FILL IN:  Option #(FILL IN) is a subset that is a complement of the event.

GPT-4o mini · Answer

In this scenario, you have a total of 10 pins numbered from 1 to 10. You knocked down pins 2, 3, 5, 6, 7, and 10 in two rolls. To find the complement of the event, we need to identify the pins that were not knocked down.

The pins that were knocked down are:

First roll: 2, 3, 5, 10
Second roll: 6, 7

So the total knocked down pins are {2, 3, 5, 6, 7, 10}.

The pins that were not knocked down are:

Pin 1
Pin 4
Pin 8
Pin 9

The complement of the event (the pins that are not knocked down) is {1, 4, 8, 9}.

Now, we can check the options:

Option #1: {2, 3, 5, 6, 7, 10} (not a complement)
Option #2: {6, 7} (not a complement)
Option #3: {1, 4, 8, 9} (this is the complement)
Option #4: {2, 3, 5, 10} (not a complement)

Thus, Option #3 is the correct answer.

So, you would fill in: Option #3 is a subset that is a complement of the event.