Question

assume the random variable \\(x\\) has a binomial distribution with the given probability of obtaining a success. find the following probability, given the number of trials and the probability of obtaining a success. round your answer to four decimal places.

\\p(x = 3), n = 8, p = 0.2\\

Explanation:

Identify the given parameters

$$ n = 8,\quad p = 0.2,\quad k = 3 $$

Apply the binomial probability formula

$$ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} $$

$$ P(X = 3) = \binom{8}{3} (0.2)^3 (0.8)^5 $$

Calculate the final value

$$ \binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 $$

$$ P(X = 3) = 56 \times 0.008 \times 0.32768 = 0.14680064 \approx 0.1468 $$

Answer:

Assume the random variable \(X\) has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.

\(P(X = 3), n = 8, p = 0.2\)

Answer: <blank>0.1468</blank>