A binomial probability experiment is conducted with the given parameters. Compute the probability of \( x \) successes in the \( n \) independent trials of the experiment. \( n=60, p=0.05, x=2 \) \( P(2)=\square \) (Do not round until the final answer. Then round to four decimal places as needed.)

To compute the probability of \( x = 2 \) successes in \( n = 60 \) independent trials with a success probability of \( p = 0.05 \), we can use the binomial probability formula: \[ P(x) = \binom{n}{x} p^x (1-p)^{n-x} \] where \( \binom{n}{x} \) is the binomial coefficient calculated as \( \frac{n!}{x!(n-x)!} \). Plugging in the values: 1. Calculate the binomial coefficient: \[ \binom{60}{2} = \frac{60!}{2!(60-2)!} = \frac{60 \times 59}{2 \times 1} = 1770 \] 2. Calculate \( p^x \): \[ p^2 = (0.05)^2 = 0.0025 \] 3. Calculate \( (1-p)^{n-x} \): \[ (1-p)^{58} = (0.95)^{58} \] Now, we can calculate \( (0.95)^{58} \): Using a calculator, we find \( (0.95)^{58} \approx 0.2460 \). 4. Now combine all parts to find \( P(2) \): \[ P(2) = 1770 \times 0.0025 \times 0.2460 \approx 0.2175 \] So, rounding to four decimal places, the probability \( P(2) \) is: \[ P(2) \approx 0.2175 \]