Step 1:
First, we need to recall the formula for the binomial probability distribution, which is given by:
\[P(x; n, \pi) = \binom{n}{x} \pi^x (1-\pi)^{n-x}\]
where:
- \(P(x; n, \pi)\) is the probability of getting exactly \(x\) successes in \(n\) trials,
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