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:

  • Total possible outcomes: A 12-sided die has 12 faces, so the total number of possible outcomes is 12.

  • 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:

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

Substituting the values: P(rolling a number greater than 18)=012=0P(\text{rolling a number greater than 18}) = \frac{0}{12} = 0

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?

  1. What is the probability of rolling a number less than 5 on a 12-sided die?
  2. If a die has 20 sides, what would the probability be of rolling a number greater than 18?
  3. How can the probability formula be adjusted for dependent events?
  4. What is the probability of rolling a prime number on a 12-sided die?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Theoretical Probability
Dice Probability

Formulas

P(Event) = Number of favorable outcomes / Total possible outcomes

Theorems

-

Suitable Grade Level

Grades 6-8