Consider a binomial experiment with 5 trials and p=0.4.a. Compute the probability of 1 success, f(1)

To compute the probability of 1 success in a binomial experiment with 5 trials and p=0.4, we can use the binomial probability formula. The formula is:

f(k) = (n choose k) * p^k * (1-p)^(n-k)

where f(k) is the probability of k successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient.

In this case, we want to find f(1), which represents the probability of 1 success. Plugging in the values into the formula, we have:

f(1) = (5 choose 1) * 0.4^1 * (1-0.4)^(5-1)

To calculate (5 choose 1), we use the formula:

(5 choose 1) = 5! / (1! * (5-1)!)

Simplifying this expression, we get:

(5 choose 1) = 5! / (1! * 4!)

Calculating the factorials, we have:

(5 choose 1) = 5 / (1 * 4) = 5

Now, we can substitute the values back into the original formula:

f(1) = 5 * 0.4^1 * (1-0.4)^(5-1)

Simplifying further, we have:

f(1) = 5 * 0.4 * 0.6^4

Calculating the values, we get:

f(1) = 5 * 0.4 * 0.1296

Finally, we can multiply the values together to find the probability:

f(1) = 0.2592

Therefore, the probability of 1 success in this binomial experiment is 0.2592.