Answer :
Answers:
- probability = 5/11
- probability = 6/11
- probability = 6/11
- probability = 3/11
- False
- False
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Explanations
Problem 1
The sample space is the set of all possible outcomes. In this situation, the sample space would be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. In short it's the set of whole numbers from 1 to 11 including both endpoints.
Because we're only interested in even numbers, the event space is {2, 4, 6, 8, 10}.
There are A = 5 items in the event space out of B = 11 items in the sample space. That leads to the probability A/B = 5/11 which is the answer to problem 1.
5/11 = 0.4545... where the "45" repeats forever
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Problem 2
Refer to the previous problem. The sample space is the same, but the event space is now {1,3,5,7,9,11} since we focus on odd numbers now.
There are A = 6 items in the event space out of B = 11 items total.
A/B = 6/11 is the answer.
Notice how 5/11 and 6/11 add up to 11/11 = 1. It tells us that the answers to problems 1 and 2 are complementary probability values. One or the other event must happen.
6/11 = 0.5454... where the "54"s repeat forever.
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Problem 3
Refer to problem 1 to see the sample space. The event space would be {6, 7, 8, 9, 10, 11}
There are A = 6 items in the event space out of B = 11 items total. We arrive at the same answer as problem 2.
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Problem 4
The event space is now {1, 2, 3} showing there are A = 3 ways to get something in the event space out of B = 11 items in the sample space.
We arrive at A/B = 3/11
3/11 = 0.2727... where the "27"s repeat forever.
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Problem 5
The claim is that it's impossible to roll a "6", which is a false claim. It's possible to roll this number since it's in the sample space. In other words, it's between 1 and 11.
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Problem 6
The term "definitely" is the same as saying "it's 100% certain". However, we are not guaranteed to roll something less than 9 since we could roll either 9, 10, or 11. This is why the claim "You will definitely roll a number less than 9" is false
Are we more likely to roll something less than 9? Yes. This is because the subset {1, 2, 3, 4, 5, 6, 7, 8} simply has more items compared to {9, 10, 11}.