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