Math Problem Statement

A​ 12-sided die is rolled. The set of equally likely outcomes is​ {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling

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Part 1

The probability of rolling

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11

is

enter your response here.

​(Type an integer or a simplified​ fraction.)

Solution

To find the probability of rolling an 11 on a 12-sided die, we use the formula for probability:

P(event)=Number of favorable outcomesTotal number of possible outcomesP(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

In this case:

  • Favorable outcome: Rolling an 11 (which is just 1 specific outcome).
  • Total possible outcomes: There are 12 sides on the die, so there are 12 possible outcomes.

Thus, the probability of rolling an 11 is:

P(11)=112P(11) = \frac{1}{12}

So, the probability of rolling an 11 is 112\frac{1}{12}.

Do you want more details on this?

Here are some related questions:

  1. What is the probability of rolling an even number on the same die?
  2. What is the probability of rolling a number greater than 9?
  3. What is the probability of rolling a number less than 5?
  4. What is the probability of rolling a prime number?
  5. What is the probability of rolling a 6 or a 12?

Tip: When calculating probabilities, always make sure to count the number of favorable outcomes and compare them to the total outcomes.

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Math Problem Analysis

Mathematical Concepts

Probability
Equally Likely Outcomes

Formulas

P(event) = Number of favorable outcomes / Total number of possible outcomes

Theorems

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Suitable Grade Level

Grades 6-8