Question
Assume that a procedure yields a binomial distribution with a trial repeated
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)=
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)=
Answers
GPT-4o mini
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.
\[
P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}
\]
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.