Math Problem Statement

A die is thrown once. Find the probability of getting a number less than 7

Solution

A standard die has six faces, numbered from 1 to 6. To find the probability of getting a number less than 7 when a die is thrown once, we need to consider the total number of possible outcomes and the number of favorable outcomes.

  1. Total possible outcomes: Since the die has six faces, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

  2. Favorable outcomes: All the numbers on the die (1, 2, 3, 4, 5, and 6) are less than 7. So, there are 6 favorable outcomes.

The probability PP of getting a number less than 7 is given by the ratio of the number of favorable outcomes to the total number of possible outcomes: P(number less than 7)=Number of favorable outcomesTotal number of possible outcomesP(\text{number less than 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

Substituting the values: P(number less than 7)=66=1P(\text{number less than 7}) = \frac{6}{6} = 1

Therefore, the probability of getting a number less than 7 when a die is thrown once is 11 or 100%100\%.

Would you like more details or have any questions?

Here are some questions you might want to ask:

  1. What is the probability of rolling an even number on a die?
  2. How do you calculate the probability of rolling a specific number on a die?
  3. What is the probability of rolling a number greater than 4 on a die?
  4. How can probabilities be expressed in different forms (fractions, decimals, percentages)?
  5. What is the probability of rolling a prime number on a die?

Tip: When dealing with probabilities, always ensure the total number of possible outcomes is correctly identified, as this forms the basis of calculating accurate probabilities.

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Math Problem Analysis

Mathematical Concepts

Probability

Formulas

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Theorems

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Suitable Grade Level

Grades 4-6