Math Problem Statement
A fair six-sided number cube (die) is rolled. Find the probability of getting less than a 6.
Solution
A fair six-sided die has numbers 1, 2, 3, 4, 5, and 6 on it. The probability of an event is calculated as:
In this case, you want to find the probability of rolling a number less than 6. The favorable outcomes are 1, 2, 3, 4, and 5, which are 5 possible outcomes.
The total number of possible outcomes is 6 (since the die has 6 faces).
Thus, the probability of getting a number less than 6 is:
This simplifies to approximately:
So, the probability is or approximately 83.33%.
Would you like further details or have any questions?
Here are 5 related questions:
- What is the probability of rolling a number greater than 4 on a six-sided die?
- If you roll two six-sided dice, what is the probability of both showing a number less than 6?
- How does the probability change if we roll an eight-sided die instead?
- What is the probability of rolling an even number on a six-sided die?
- What is the probability of rolling a number less than or equal to 3 on a six-sided die?
Tip: When solving probability problems, always check how many outcomes meet the condition you’re interested in and compare that to the total number of possible outcomes.
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Math Problem Analysis
Mathematical Concepts
Probability
Basic Counting Principle
Formulas
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 5-7