A dog completes a trick 8 out of 20 times.
What is the formula for the binomial distribution
The formula for the binomial distribution is:
P(X = k) = nCk * p^k * (1-p)^(n-k)
where:
P(X = k) is the probability of getting exactly k successes,
n is the number of trials,
k is the number of successful outcomes,
p is the probability of success in a single trial, and
(1-p) is the probability of failure in a single trial.
In this case, since the dog completes a trick 8 out of 20 times, the values are:
n = 20 (number of trials),
k = 8 (number of successful outcomes),
p = 8/20 = 0.4 (probability of success in a single trial),
1-p = 1 - 0.4 = 0.6 (probability of failure in a single trial).