Assume that a procedure yields a binomial distribution with a trial repeated

Question

times. Use either the binomial probability formula (or technology) to find the probability of
successes given the probability
of success on a single trial.

(Report answer accurate to 4 decimal places.)


P(X=k)=

Answer 1

To calculate the probability of getting \( k \) successes in a binomial distribution, we can use the binomial probability formula:

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

where:

• \( n \) = total number of trials,
• \( k \) = number of successes,
• \( p \) = probability of success on a single trial,
• \( \binom{n}{k} \) = "n choose k" = \( \frac{n!}{k!(n-k)!} \)

Please provide the values for \( n \), \( k \), and \( p \), and I will compute \( P(X = k) \) for you.