quisite Week 5 Homework
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Evaluate ${ }_{n} C_{x} p^{x}(1-p)^{n-x}$ for $n=6, p=0.2, x=3$.

The answer is $\square$.
(Round to four decimal places as needed.)

Step 1 ：Given values are \(n = 6\), \(p = 0.2\), and \(x = 3\).

Step 2 ：Calculate combinations, which is \({ }_{n} C_{x}\). In this case, it is \({ }_{6} C_{3} = 20\).

Step 3 ：Calculate powers, which are \(p^{x}\) and \((1-p)^{n-x}\). In this case, they are \(0.2^{3} = 0.008\) and \((1-0.2)^{6-3} = 0.512\).

Step 4 ：Calculate the result by multiplying the combinations and the powers. The result is \(20 \times 0.008 \times 0.512 = 0.08192\).

Step 5 ：This is the probability of getting exactly 3 successes in 6 trials, when the probability of success on each trial is 0.2.

Step 6 ：Final Answer: The answer is \(\boxed{0.08192}\).