Task 3. (15 points) At the quality control department of an oil refinery, Engineer Valentina Ivanovna received a research object consisting of about 200 oil samples (a container designed for 200 samples, which was almost completely filled). Each sample has certain characteristics in terms of sulfur content - either low-sulfur or high-sulfur, and density - either light or heavy. The relative frequency (statistical probability) that a randomly selected sample will be a heavy oil sample is $\frac{1}{9}$. The relative frequency that a randomly selected sample will be a light low-sulfur oil sample is $\frac{11}{18}$. How many high-sulfur oil samples does the object contain, if there were no low-sulfur samples among the heavy oil samples?
# Solution.

Let's determine the exact number of oil samples. It is known that the relative frequency of a sample being a heavy oil sample is $\frac{1}{9}$. The number closest to 200 that is divisible by 9 is 198. Therefore, the total number of samples in the container is 198. The samples of high-sulfur oil consist of all heavy oil samples ($198: 9=22$) and a portion of the light oil samples. Let's find out how many high-sulfur oil samples are among the light oil samples. The total number of light oil samples is $198: 9 \cdot 8=176$. Among them, the samples of low-sulfur oil constitute $\frac{11}{18}$ of the total, which is 121. Therefore, the number of high-sulfur light oil samples is 55. Thus, the total number of high-sulfur oil samples is: $22+55=77$.

Answer. 77.