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.





(1 point)
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}

Answer 1

In probability, the complement of an event consists of all the outcomes that are not part of the event. In this case, the event consists of the pins that were knocked down, which are {2, 3, 5, 6, 7, 10}.

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

To find the complement of the event (the pins that were not knocked down), we subtract the knocked-down pins from the total set:

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

Knocked down pins: {2, 3, 5, 6, 7, 10}

Remaining (not knocked down) pins = {1, 4, 8, 9}

Now, let's evaluate the options provided:

Option #1: {2, 3, 5, 6, 7, 10} - This set contains the knocked down pins, so it is not a complement.

Option #2: {6, 7} - This set contains knocked down pins, so it is not a complement.

Option #3: {1, 4, 8, 9} - This set contains the pins that were not knocked down, so it is indeed a complement.

Option #4: {2, 3, 5, 10} - This set contains knocked down pins, so it is not a complement.

Therefore, the correct answer is **Option #3: {1, 4, 8, 9}**.