Assume that a procedure yields a binomial distribution with $n=4$ trials and a probability of success of $p=0.30$. Use a binomial probability table to find the probability that the number of successes $x$ is exactly 1 . Click on the icon to view the binomial probabilities table. $P(1)=\square$ (Round to three decimal places as needed.)

Step 1 ：We are given a binomial distribution with $n=4$ trials and a probability of success of $p=0.30$. We are asked to find the probability that the number of successes $x$ is exactly 1.

Step 2 ：The binomial probability formula is given by: $P(x; n, p) = \binom{n}{x} * p^x * (1 - p)^{n - x}$, where $P(x; n, p)$ is the probability of getting exactly $x$ successes in $n$ trials, $\binom{n}{x}$ is the number of combinations of $n$ items taken $x$ at a time, $p$ is the probability of success on any given trial, and $x$ and $n - x$ are the numbers of successes and failures, respectively.

Step 3 ：Substituting the given values into the formula, we get $P(1; 4, 0.30) = \binom{4}{1} * 0.30^1 * (1 - 0.30)^{4 - 1}$.

Step 4 ：Solving this expression, we get a probability of approximately 0.4116.

Step 5 ：However, the question asks for the answer to be rounded to three decimal places. Therefore, the final answer should be 0.412.

Step 6 ：Final Answer: $P(1)=\boxed{0.412}$