Determine the probability if you were rolling a 11 sided die.

1) What is the probability of rolling an even number?

2) What is the probability of rolling an odd number?

3) What is the probability of rolling a number higher than 5?

4) What is the probability of rolling an odd number less than 4?

5) True/False: It is impossible to roll a 6.

6) True/False: You will definitely roll a number less than 9.

A 12 sided dice

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}.