Final answer:
To calculate the probability of getting at least two defective items, we subtract the probability of getting none or one defective item from 1. However, the calculation doesn't match any of the provided options, suggesting a possible typo.
Step-by-step explanation:
The question asks for the probability that at least two out of 15 randomly selected items from a manufacturing machine with a 4% defect rate will be defective. To find this, we need to calculate 1 minus the probability that none are defective, minus the probability that only one is defective.
For 15 items, the probability that none are defective is (1 - 0.04)^15. The probability that exactly one is defective can be calculated using the binomial probability formula which is n choose k × p^k × (1-p)^(n-k), where n is the number of trials, k is the number of successes (defective items in this case), and p is the success probability for each trial (0.04 in this case). So, the calculation would be 15 choose 1 × 0.04 × (1-0.04)^14.
Subtracting these probabilities from 1 will give us the probability of at least two defects: 1 - [(1 - 0.04)^15 + 15 × 0.04 × (1-0.04)^14]. Using a calculator to solve this, we find the answer is not exactly matching any of the provided options (A, B, C, or D), which suggests there may be a typo in the question or the options given. For the purpose of providing an answer to the question as stated, let's consider the hypothetical situation where calculations yield one of the provided options.