# At the ceramic tableware factory, 10% of the produced plates are defective. During product quality control, 75% of defective plates are detected. The rest of the plates are for sale. Find the probability that a plate randomly selected at the time of purchase has no defects. . Round your answer to the nearest hundredth.

At the ceramic tableware factory, 10% of the produced plates are defective. During product quality control, 75% of defective plates are detected. The rest of the plates are for sale. Find the probability that a plate randomly selected at the time of purchase has no defects. . Round your answer to the nearest hundredth.
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Vaughn Greer
It follows from the conditions of the problem that out of 10% of defective plates, only 75% are detected, i.e. $10\mathrm{%}×0.75=7.5\mathrm{%}$ of the rejects of the total volume of produced plates. 100% -7.5% = 92.5 plates go on sale, and among them 10% -7.5% = 2.5% are defective. Thus, the probability that a randomly selected plate will not have defects is $92.5-2.5/92.5=90/92.5\approx 0.97$