Probability of at Least One Six in 4 Dice Rolls
“At least one” includes one, two, three or four sixes. Adding each of those cases works, but it is shorter to calculate the complement: the chance of rolling no sixes, then subtract that from 1.
The question
If a fair six-sided die is rolled 4 times, what is the probability that at least one roll is a six?
These calculations use a probability model that matches the stated assumptions. If the events are not independent or the chance changes between trials, the binomial formula may not describe the real situation.
Step-by-step solution
- The probability of not rolling a six on one roll is 5/6.
- The rolls are independent, so the probability of no sixes in all 4 rolls is (5/6)⁴ = 625/1296 ≈ 0.482253.
- Use the complement: P(at least one six) = 1 − P(no sixes) = 1 − 625/1296.
- Subtract to get 671/1296 ≈ 0.517747.
Answer: The probability is about 0.5177, or 51.77%. The complement method includes every outcome with one or more sixes without listing them separately.
Check the result with a calculator
Open the at-least-one calculator with p = 1/6 and 4 rolls. You can change the inputs to compare a different number of trials, success probability or target count.
For other probability questions, use the binomial distribution calculator for exact, cumulative and range outcomes, or browse the full calculator directory.