What is the probability of rolling a number greater than 4 on a fair 6-sided die?
Understand the Problem
The question is asking for the probability of rolling a number greater than 4 on a 6-sided die. To solve this, we will identify the favorable outcomes (rolling a 5 or 6) and divide by the total number of outcomes (which is 6).
Answer
The probability is $\frac{1}{3}$.
Answer for screen readers
The probability of rolling a number greater than 4 on a 6-sided die is $\frac{1}{3}$.
Steps to Solve
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Identify Total Outcomes
A 6-sided die has 6 possible outcomes when rolled: {1, 2, 3, 4, 5, 6}. Therefore, the total number of outcomes is 6. -
Identify Favorable Outcomes
We want to find the probability of rolling a number greater than 4. The favorable outcomes for this condition are {5, 6}. So, there are 2 favorable outcomes. -
Calculate Probability
To find the probability, we use the formula:
$$ P(\text{rolling a number greater than 4}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} $$
Substituting in our numbers, we get:
$$ P(\text{greater than 4}) = \frac{2}{6} $$ -
Simplify the Fraction
To simplify the fraction $\frac{2}{6}$, we divide the numerator and denominator by their greatest common divisor, which is 2:
$$ P(\text{greater than 4}) = \frac{1}{3} $$
The probability of rolling a number greater than 4 on a 6-sided die is $\frac{1}{3}$.
More Information
The probability calculated shows that when you roll a standard die, there's a 33.33% chance (or approximately one-third) that the number shown will be greater than 4. This offers insight into basic probability calculations involving fairness in games of chance.
Tips
- Ignoring total outcomes: Ensure you always count all possible outcomes correctly.
- Favorable outcomes misunderstanding: Misidentify which outcomes meet the criteria. Double-check that you've correctly identified the numbers greater than 4.
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