To find the probability that at least one of the 8 items chosen will have a defect, we can approach this problem using the complement rule. The complement rule states that the probability of an event happening is $1 -$ the probability of it not happening.

Step-by-step Solution:

1. Defining the Problem: The probability of an item being defective is 6%, or $0.06$. Therefore, the probability that an item is not defective is $1 - 0.06 = 0.94$.

2. Finding the Complement: The probability that none of the 8 items are defective (i.e., all 8 items are non-defective) is the product of the probability that each individual item is non-defective: $P(\text{none defective}) = (0.94)^8$

3. Calculation: Now, calculate $0.94^8$: $0.94^8 \approx 0.6243$

4. Finding the Desired Probability: The probability that at least one of the 8 items is defective is the complement of the probability that none are defective: $P(\text{at least one defective}) = 1 - P(\text{none defective}) = 1 - 0.6243 = 0.3757$

Thus, the probability that at least one of the 8 items is defective is approximately $0.3757$.

Final Answer:

$P(\text{at least one defective}) \approx 0.3757$

Would you like further details or have any other questions?

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Here are 5 related questions you might find interesting:

1. What is the probability that exactly two of the items are defective?
2. How would the probability change if the defect rate increased to 10%?
3. If the sample size increased to 12 items, what would be the probability of at least one defect?
4. What is the probability that none of the 8 items are defective?
5. How do probabilities change when choosing items with replacement versus without?

Tip: Understanding complements is a powerful tool in probability, especially when calculating "at least one" events!