Problem

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.)

Solution

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 \(\boxed{0.042}\).

From Solvely APP
Source: https://solvelyapp.com/problems/8702/

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