The probability that a dolphin successfully performs the trick is 8 out of 20 attempts.et X = the number of times the dolphin successfully performs a trick. What is the formula for the binomial distribution?
The formula for the binomial distribution is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of getting exactly k successes in n attempts.
C(n, k) is the binomial coefficient, which calculates the number of ways to choose k successes from n trials.
p is the probability of success in a single trial.
(1-p) is the probability of failure in a single trial.
k is the number of successes to be obtained.
n is the total number of independent trials.