point(s) possible
A binomial probability experiment is conducted with the given parameters. Compute the probability of $x$ successes in the $n$ independent trials of the experiment.
\[
n=9, p=0.8, x \leq 3
\]

The probability of $x \leq 3$ successes is $\square$. (Round to four decimal places as needed.)
Time Remaining: 00:33:53

Step 1 ：A binomial probability experiment is conducted with the parameters \(n=9\), \(p=0.8\), and we are asked to compute the probability of \(x \leq 3\) successes.

Step 2 ：We calculate the probability for each value of \(x\) in the range 0 to 3 using the binomial probability mass function (pmf).

Step 3 ：The calculated probabilities for \(x=0\), \(x=1\), \(x=2\), and \(x=3\) are approximately \(5.12 \times 10^{-7}\), \(1.84 \times 10^{-5}\), \(0.000294912\), and \(0.002752512\) respectively.

Step 4 ：We sum these probabilities to get the total probability of \(x \leq 3\).

Step 5 ：The total probability is approximately \(0.003066368\).

Step 6 ：We round this to four decimal places as needed, giving a final answer of \(\boxed{0.0031}\).