A binomial experiment with probability of success $p=0.88$ and $n=7$ trials is conducted. What is the probability that the experiment results in 4 or fewer successes?
Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)
Answer
Final Answer: The probability that the experiment results in 4 or fewer successes is approximately \(\boxed{0.042}\).
Step 1 ：We are given a binomial experiment with a probability of success \(p=0.88\) and \(n=7\) trials. We are asked to find the probability that the experiment results in 4 or fewer successes.
Step 2 ：This can be calculated by summing up the probabilities of getting 0, 1, 2, 3, and 4 successes.
Step 3 ：The formula for the probability of getting exactly k successes in n trials is given by: \[P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\] where \(C(n, k)\) is the binomial coefficient, \(p\) is the probability of success, and \(n\) is the number of trials.
Step 4 ：Using this formula, we can calculate the probability of getting 4 or fewer successes.
Step 5 ：The calculated probability is approximately 0.04163883909119999.
Step 6 ：Final Answer: The probability that the experiment results in 4 or fewer successes is approximately \(\boxed{0.042}\).
