A die is rolled 9 times. Find the probability of rolling exactly 1 four.

Step 1 ：We are given a problem where a die is rolled 9 times and we need to find the probability of rolling exactly 1 four. This is a classic example of a problem that can be solved using the binomial probability formula.

Step 2 ：The binomial probability formula is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the combination of n items taken k at a time, p is the probability of success on a single trial, n is the number of trials, and k is the number of successes.

Step 3 ：In this case, the die is rolled 9 times (n=9), we want to find the probability of rolling exactly 1 four (k=1), and the probability of rolling a four on a single roll is 1/6 (p=1/6).

Step 4 ：Substituting the given values into the formula, we get \(P(X=1) = C(9, 1) * (0.16666666666666666^1) * ((1-0.16666666666666666)^(9-1))\).

Step 5 ：Calculating the above expression, we get a probability of approximately 0.349.

Step 6 ：Thus, the probability of rolling exactly 1 four when a die is rolled 9 times is approximately \(\boxed{0.349}\).