To determine which of the given options is a subset that is a complement of the event, we first need to identify the total set of pins and the pins that were knocked down in the mentioned rolls.
There are 10 bowling pins, which we can denote as the set: \[ \text{Pins} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} \]
In the first roll, the following pins were knocked down: \[ \text{Knocked Down (Roll 1)} = {1, 5, 7, 9} \]
In the second roll, the following pins were knocked down: \[ \text{Knocked Down (Roll 2)} = {4, 8} \]
Now, we can combine these sets to find out all the pins that were knocked down in total: \[ \text{Knocked Down Total} = {1, 5, 7, 9, 4, 8} = {1, 4, 5, 7, 8, 9} \]
Next, we find the complement of the event by determining the pins that were not knocked down: \[ \text{Pins Not Knocked Down} = \text{Pins} - \text{Knocked Down Total} = {2, 3, 6, 10} \]
Now, we will evaluate each of the options to see which one is a subset of the pins that were not knocked down (the complement):
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Option #1: {3, 4, 6, 9}
- This set includes 4 and 9, which were knocked down. So this is not a subset of the complement.
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Option #2: {2, 3, 6, 10}
- All pins in this set (2, 3, 6, and 10) are in the set of pins not knocked down. So this is a subset of the complement.
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Option #3: {1, 4, 5, 7, 8, 9}
- All pins in this set (1, 4, 5, 7, 8, and 9) were knocked down, so this is not a subset of the complement.
Given this analysis, the correct option that is a subset of the event's complement is:
Option 2
1 answer