What is the probability of rolling doubles?
Understand the Problem
The question is asking for the probability of rolling doubles with a pair of dice. To find this, we need to consider the total number of possible outcomes when rolling two dice and the specific outcomes that result in doubles.
Answer
The probability of rolling doubles with a pair of dice is $\frac{1}{6}$.
Answer for screen readers
The probability of rolling doubles with a pair of dice is $\frac{1}{6}$.
Steps to Solve
- Identify Total Outcomes
When rolling two dice, each die has 6 faces. Therefore, the total number of outcomes when rolling two dice is calculated by multiplying the outcomes of each die:
$$ \text{Total outcomes} = 6 \times 6 = 36 $$
- Identify Doubles Outcomes
Doubles occur when both dice show the same number. The possible outcomes for doubles are: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). This gives us a total of:
$$ \text{Doubles outcomes} = 6 $$
- Calculate Probability
To find the probability of rolling doubles, we divide the number of doubles outcomes by the total number of outcomes:
$$ \text{Probability of doubles} = \frac{\text{Doubles outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6} $$
The probability of rolling doubles with a pair of dice is $\frac{1}{6}$.
More Information
The probability of rolling doubles is relatively low but common in many games involving dice. Each die's independence allows for a variety of outcomes, but there are fewer ways to match both dice compared to the total possible outcomes.
Tips
- Confusing total outcomes with favorable outcomes: Ensure you distinguish between the total number of outcomes (36) and the number of doubles (6).
- Not simplifying the fraction: It’s important to reduce the fraction $$\frac{6}{36}$$ to its simplest form, which is $$\frac{1}{6}$$.
