Find the probability of at least one 3 in 6 rolls of a fair die. Round to three decimal places.
The probability of rolling at least one 3 in 6 rolls of a fair die can be calculated using the complement rule.
The complement of rolling at least one 3 is rolling no 3s in 6 rolls. Since each roll is independent, the probability of not rolling a 3 on any one roll is 5/6. Therefore, the probability of not rolling a 3 in 6 rolls is (5/6)^6.
To find the probability of rolling at least one 3, we subtract the probability of rolling no 3s from 1:
P(at least one 3) = 1 - P(no 3s)
P(at least one 3) = 1 - (5/6)^6
Calculating this expression:
P(at least one 3) ≈ 1 - 0.334 = 0.666.
Rounded to three decimal places, the probability of rolling at least one 3 in 6 rolls of a fair die is 0.666.