A manufacturing machine has a 10% defect rate. If 6 items are chosen at random, what is the probability that at least one will have a defect?

Step 1 ：We are given a manufacturing machine with a 10% defect rate. We are asked to find the probability that at least one out of 6 randomly chosen items will have a defect.

Step 2 ：This is a problem of probability and can be solved using the concept of binomial distribution. The probability of at least one defective item is equal to 1 minus the probability of no defective items.

Step 3 ：The probability of no defective items can be calculated using the formula for binomial distribution: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) 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, and k is the number of successes.

Step 4 ：In this case, n=6 (number of items chosen), p=0.1 (probability of a defect), and k=0 (we are looking for the probability of no defects).

Step 5 ：Using these values in the formula, we find that the probability of no defects is approximately 0.531441.

Step 6 ：Subtracting this from 1 gives us the probability of at least one defect, which is approximately 0.46855899999999995.

Step 7 ：Final Answer: The probability that at least one item will have a defect is approximately \(\boxed{0.4686}\).