A binomial probability experiment is conducted with the given parameters. Compute the probability of $x$ successes in the $\mathrm{n}$ independent trials of the experiment. \[ n=9, p=0.5, x \leq 3 \] The probability of $x \leq 3$ successes is (Round to four decimal places as needed.)

Step 1 ：We are given a binomial probability experiment with parameters $n=9$, $p=0.5$, and we are asked to compute the probability of $x \leq 3$ successes.

Step 2 ：The binomial probability formula is given by: \[P(x; n, p) = \binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}\] 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 $x$ is the number of successes.

Step 3 ：In this case, we are asked to find the probability of $x \leq 3$ successes. This means we need to find the sum of the probabilities of getting exactly 0, 1, 2, or 3 successes.

Step 4 ：Using the given parameters and the binomial probability formula, we calculate the sum of the probabilities for $x=0$, $x=1$, $x=2$, and $x=3$.

Step 5 ：The calculated probability is 0.25390625.

Step 6 ：Rounding to four decimal places as needed, the final answer is \(\boxed{0.2539}\).