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A binomial probability experiment is conducted with the given parameters. Compute the probability of $x$ successes in the $n$ independent trials of the experiment
\[
\mathrm{n}=10, \mathrm{p}=0.65, \mathrm{x}=6
\]
\[
P(6)=\square
\]
(Do not round until the final answer. Then round to four decimal places as needed)
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Step 1 ：We are given that the number of trials \(n = 10\), the probability of success \(p = 0.65\), and the number of successes \(x = 6\).

Step 2 ：We use the binomial probability formula to calculate the probability of getting exactly 6 successes in 10 trials. The formula is \(P(x) = C(n, x) \cdot p^x \cdot (1-p)^{n-x}\), where \(C(n, x)\) is the number of combinations of \(n\) items taken \(x\) at a time.

Step 3 ：We calculate the number of combinations \(C(n, x) = C(10, 6) = 210\).

Step 4 ：We calculate \(p^x = 0.65^6 = 0.07541889062500001\).

Step 5 ：We calculate \((1-p)^{n-x} = (1-0.65)^{10-6} = 0.015006249999999997\).

Step 6 ：We substitute these values into the binomial probability formula to get the probability \(P(6) = 210 \cdot 0.07541889062500001 \cdot 0.015006249999999997 = 0.2376684927626953\).

Step 7 ：We round the final answer to four decimal places to get \(\boxed{0.2377}\).