find the probability of at least one 3 in 4 rolls of a fair die. round to three decimals places
To find the probability of at least one 3 in 4 rolls of a fair die, we can find the complement of the event "no 3s in 4 rolls".
The probability of rolling a number other than 3 on a fair die is 5/6.
Thus, the probability of rolling a number other than 3 in one roll is (5/6).
The probability of not rolling a 3 in four rolls is (5/6) * (5/6) * (5/6) * (5/6) = (5/6)^4.
To find the probability of at least one 3 in 4 rolls, we subtract the probability of rolling no 3s from 1.
Probability of at least one 3 in 4 rolls = 1 - (5/6)^4.
Calculating this expression:
1 - (5/6)^4 = 1 - (625/1296) ≈ 1 - 0.482 = 0.518.
Rounding to three decimal places, the probability of at least one 3 in 4 rolls of a fair die is approximately 0.518.