A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of \( x \) successes in the \( n \) independent trials of the experiment. \( n=7, p=0.35, x<4 \) \( P(X<4)=\square \) (Round to four decimal places as needed.)

To find \( P(X < 4) \) in a binomial probability experiment with \( n = 7 \) trials and a success probability \( p = 0.35 \), you can use a binomial probability calculator or software like Python, R, or even a scientific calculator that supports binomial distributions. First, calculate the probabilities for \( x = 0, 1, 2, \) and \( 3 \). The formula for a single binomial probability is: \[ P(X = x) = \binom{n}{x} p^x (1 - p)^{n - x} \] Thus, sum these probabilities: \[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \] After performing the calculations (or using technology), you will find that \( P(X < 4) \approx 0.7466 \). Now, have fun trying it out on different trial values or probabilities to see how it affects the overall outcome! Working with binomial distributions is like playing with a probability playground!