Final answer:
The probability of exactly 4 successes in a binomial distribution can be calculated using the formula P(X=k) = C(n,k) * p^k * (1-p)^(n-k), where p is the probability of success, n is the number of trials, and k is the number of successes we want to calculate the probability for.
Step-by-step explanation:
To calculate the probability of exactly 4 successes in a binomial distribution, we can use the formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- C(n,k) is the number of combinations of n items taken k at a time
- p is the probability of success
- n is the number of trials
- k is the number of successes we want to calculate the probability for
By substituting the values into the formula, we get:
P(X=4) = C(6,4) * 0.8^4 * (1-0.8)^(6-4) = 15 * 0.8^4 * 0.2^2 = 0.24576
Therefore, the probability of exactly 4 successes in a binomial distribution with a probability of success of 0.8 and 6 trials is 0.24576.