Math Problem Statement
Use the theoretical probability formula to solve the following problem. Express the probability as a fraction reduced to lowest terms.
A 12-sided die is rolled. The set of equally likely outcomes is
StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 comma 11 comma 12 EndSet .{1,2,3,4,5,6,7,8,9,10,11,12}.
Find the probability of rolling a number greater than
Solution
The problem asks to find the probability of rolling a number greater than 18 on a 12-sided die. However, the maximum number on a 12-sided die is 12, so it is impossible to roll a number greater than 18.
Probability Calculation:
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Total possible outcomes: A 12-sided die has 12 faces, so the total number of possible outcomes is 12.
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Favorable outcomes: There are no numbers greater than 18 on a 12-sided die, so the number of favorable outcomes is 0.
Formula for Probability:
Substituting the values:
So, the probability of rolling a number greater than 18 is 0.
Would you like to explore more probability-related questions or details about how the theoretical probability formula works?
- What is the probability of rolling a number less than 5 on a 12-sided die?
- If a die has 20 sides, what would the probability be of rolling a number greater than 18?
- How can the probability formula be adjusted for dependent events?
- What is the probability of rolling a prime number on a 12-sided die?
- How do you calculate the probability of multiple independent events happening together?
Tip: Always check the possible outcomes first, especially in cases where the numbers you're interested in might exceed the maximum values on the die.
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Math Problem Analysis
Mathematical Concepts
Probability
Theoretical Probability
Dice Probability
Formulas
P(Event) = Number of favorable outcomes / Total possible outcomes
Theorems
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Suitable Grade Level
Grades 6-8
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