A single die is rolled three times. A success is considered rolling a 6. What is the probability of rolling at least one 6?
at least one means not none
p = 1 - (5/6)^3
I think (1-5/6)^3
I am wrong, use R Scott reply
To find the probability of rolling at least one 6 when a single die is rolled three times, we will calculate the probability of the complement event (not rolling any 6s) and subtract it from 1.
The probability of not rolling a 6 on a single roll is 5/6, as there are five other outcomes (numbers 1 to 5) out of six possible outcomes on a standard die.
So, the probability of not rolling a 6 on all three rolls is (5/6) * (5/6) * (5/6). Since these events are independent, we can multiply the probabilities together.
The probability of rolling at least one 6 is therefore 1 minus the probability of not rolling a 6 on all three rolls:
1 - (5/6)(5/6)(5/6) = 1 - 125/216 ≈ 0.421
So, the probability of rolling at least one 6 is approximately 0.421, or 42.1%.