Problem

A binomial probability experiment is conducted with the given parameters. Compute the probability of $x$ successes in the $n$ independent trials of the experiment. $n=9, p=0.7, x \leq 3$ The probability of $x \leq 3$ successes is (Round to four decimal places as needed.) w an example Get more help - Clear all Givects angr

Solution

Step 1 :The problem is asking for the probability of getting 3 or fewer successes in a binomial experiment with 9 trials and a success probability of 0.7.

Step 2 :The binomial probability formula is: \(P(x; n, p) = C(n, x) * (p^x) * ((1 - p)^(n - x))\), where \(P(x; n, p)\) is the probability of getting exactly x successes in n trials, \(C(n, x)\) is the number of combinations of n items taken x at a time, p is the probability of success on any given trial, and x is the number of successes.

Step 3 :We need to calculate this probability for x = 0, 1, 2, and 3, and then sum these probabilities to get the final answer.

Step 4 :Given n = 9 and p = 0.7, the total probability is calculated to be approximately 0.0253.

Step 5 :\(\boxed{0.0253}\) is the final answer. The probability of getting 3 or fewer successes is approximately 0.0253.

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