A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of $x$ successes in the $\mathrm{n}$ independent trials of the experiment. \[ n=9, p=0.35, x<4 \] \[ P(X<4)= \] (Round to four decimal places as needed.)

Step 1 ：The problem is asking for the probability of less than 4 successes in a binomial experiment with 9 trials and a success probability of 0.35. This means we need to find the sum of the probabilities of 0, 1, 2, and 3 successes.

Step 2 ：The formula for the binomial probability is: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: \(P(X=k)\) is the probability of \(k\) successes, \(C(n, k)\) is the number of combinations of \(n\) items taken \(k\) at a time, \(p\) is the probability of success on a single trial, \(n\) is the number of trials, \(k\) is the number of successes.

Step 3 ：We can calculate the probabilities for 0, 1, 2, and 3 successes, and then sum these probabilities to get the final answer.

Step 4 ：The probabilities for 0, 1, 2, and 3 successes are approximately 0.0207, 0.1004, 0.2162, and 0.2716 respectively.

Step 5 ：The final probability of having less than 4 successes in a binomial experiment with 9 trials and a success probability of 0.35 is the sum of these probabilities, which is approximately 0.6089.

Step 6 ：Final Answer: The probability of having less than 4 successes is approximately \(\boxed{0.6089}\).