To determine the probability of rolling a 6 at least once when a die is rolled 4 times, we can use the complementary probability method.
First, we calculate the probability of not rolling a 6 in a single roll. Since a die has 6 faces, the probability of not rolling a 6 is:
- P(Not 6) = 5/6
Next, we find the probability of not rolling a 6 in all 4 rolls. Since each roll is independent, we multiply the probabilities:
- P(Not 6 in 4 rolls) = (5/6) ^ 4
- P(Not 6 in 4 rolls) = 625/1296
Now, to find the probability of rolling at least one 6, we subtract the probability of not rolling a 6 from 1:
- P(At least one 6) = 1 – P(Not 6 in 4 rolls)
- P(At least one 6) = 1 – 625/1296
- P(At least one 6) = (1296 – 625) / 1296
- P(At least one 6) = 671/1296
Thus, the probability of rolling a 6 at least once in 4 rolls is 671/1296, which is approximately 0.5177 or 51.77%.