What is the probability of rolling doubles with two dice?
Understand the Problem
The question is asking for the probability of rolling doubles (the same number on both dice) when rolling two six-sided dice. The approach to solve it involves calculating the total number of outcomes when rolling two dice and the number of outcomes that result in doubles.
Answer
The probability of rolling doubles is $ \frac{1}{6} $.
Answer for screen readers
The probability of rolling doubles when rolling two six-sided dice is $ \frac{1}{6} $.
Steps to Solve
- Calculate the total number of outcomes
When rolling two six-sided dice, each die has 6 faces. Thus, the total number of outcomes when rolling both dice is calculated by multiplying the number of options for each die:
$$ \text{Total Outcomes} = 6 \times 6 = 36 $$
- Identify the successful outcomes for doubles
Doubles occur when both dice show the same number. The successful outcomes (i.e., rolling doubles) are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)
This gives us a total of 6 successful outcomes.
- Calculate the probability of rolling doubles
The probability of an event is calculated by dividing the number of successful outcomes by the total number of outcomes:
$$ \text{Probability of Doubles} = \frac{\text{Successful Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} $$
- Simplify the probability
Now we can simplify the fraction:
$$ \frac{6}{36} = \frac{1}{6} $$
The probability of rolling doubles when rolling two six-sided dice is $ \frac{1}{6} $.
More Information
Rolling two six-sided dice yields a probability of $ \frac{1}{6} $ for doubles, which means that in about one out of every six rolls, you can expect to roll doubles. This is a common scenario in games involving dice, making this knowledge quite handy.
Tips
- Not counting the total outcomes correctly. Remember to multiply the outcomes for each die.
- Forgetting to list all six successful doubles outcomes.
