 Algorithms that make random choices at one probabilistic algorithms. A particular class of probabilistic algorithms is Monte Carlo algorithms. Monte Carlo algorithms always produce answers to decision problems, but a small probability remains that these answers may be incorrect. A Monte Carlo algorithm uses a sequence of tests and the probability that the algorithm answers the decision problem correctly increases as more tests are carried out. Suppose there are n0 items in a batch and the probability that an item is defective is pwhen random testing is done. To decide all items are good, n tests are required to guarantee that none of the items are defective. However a Monte Carlo algorithm can determine whether all items are good as long as some probability of error is acceptable. more steps are called or n A Monte Carlo algorithm proceeds by successively selecting items at random and testing them one by one, where the maximum number of items being tested is a pre-determined kn. When a defective item is encountered, the algorithm stops to indicate that out of the n items in a batch, there is at least one defective. If a tested item is good, the algorithm goes on to the next item. If after testing k items, no defective item is found, the algorithm concludes that all n items are good, but with a modest probability of error which is independent of n. Assuming the events of testing different items are independent, determine that the probability not even one item is defective after testing k items. Analyze the impact of n, k, and p on the probability of finding not even a defective item. As a particular case, suppose there are ten million IC chips made in a factory where the probability that an IC chip is in a perfect condition is 0.99. Based on the Monte Carlo algorithm, determine the minimum number of IC chips which need to be tested so the probability of finding not even a defective IC chip among those tested is less than one in a million