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 > 1), n = 5, p = 0.7\\

Explanation:

Identify the parameters and target probability

Using the Binomial Distribution knowledge point
We are given a binomial random variable \(X\) with:

• Number of trials: \(n = 5\)
• Probability of success: \(p = 0.7\)
• Probability of failure: \(q = 1 - p = 0.3\)

We need to find the probability \(P(X > 1)\).

Apply the complement rule

Using the Complementary Events knowledge point

$$ P(X > 1) = 1 - P(X \le 1) = 1 - [P(X = 0) + P(X = 1)] $$

Calculate the individual probabilities

Using the Binomial Distribution knowledge point

$$
LATEXBLOCK0
$$

Compute the final probability

Using the Binomial Distribution knowledge point

$$
LATEXBLOCK1
$$

Rounding to four decimal places gives \(0.9692\).

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.

\(P(X > 1), n = 5, p = 0.7\)

Answer: <blank>0.9692</blank>