Question

suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. unfortunately, 10 of the chips are defective. (a) compute the probability that two randomly selected chips are defective using conditional probability. (b) the probability that the first randomly selected chip is defective is \\( \frac { 10 } { 10,000 } = 0.001 = 0.1 \\% \\). compute the probability that two randomly selected chips are defective under the assumption of independent events. (a) the probability is 0.00000090 (round to eight decimal places as needed.) (b) the probability is 0.00000100 (round to eight decimal places as needed.) when small samples are taken from large populations without replacement, the assumption of independence does not significantly affect the probability. based on the results, what does this mean? a. the probabilities are exactly the same. b. the probabilities are very different, but the probability found assuming independent events is smaller, so it does not matter. c. the probabilities are nearly the same. d. the probabilities are very different, but the probability found assuming independent events is larger, so it does not matter

Explanation:

When dealing with probability problems involving sampling without replacement from a large population, the difference between conditional probability and the probability assuming independent events (which is a simplification) can be analyzed. Here, the probability values \(0.00000090\) (conditional probability) and \(0.00000100\) (probability assuming independent events) are very close. The key concept is that for large populations, the effect of non - replacement (which makes events dependent) is negligible in terms of probability calculation differences.

Answer:

C. The probabilities are nearly the same.