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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.

1 answer

To determine the complement of the event, we first need to identify which pins are knocked down during the two rolls.

From the first roll, the pins knocked down are:

  • 9
  • 5
  • 7
  • 1

From the second roll, the pins knocked down are:

  • 4
  • 8

Combining these, the pins that are knocked down include:

  • 1, 4, 5, 7, 8, 9

So, a total of 6 pins have been knocked down. The pins that are still standing (not knocked down) are:

  • 2
  • 3
  • 6
  • 10

The complement of the event (the pins not knocked down) is the set {2, 3, 6, 10}.

Now let's analyze the options provided:

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

  • This option includes pins 4 and 9, which are knocked down, so it's not a subset of the complement.

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

  • This option includes only pins that are not knocked down, thus it matches the complement.

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

  • This option includes all knocked down pins and is not a subset of the complement.

Therefore, the answer is:

Option #2 is a subset that is a complement of the event.