Task 3. (15 points) At the research institute, a scientific employee, Tatyana Vasilyevna, received an object for research containing about 150 oil samples (a container designed for 150 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 $\frac{2}{11}$. The relative frequency that a randomly selected sample will be a light low-sulfur oil sample is $\frac{7}{13}$. 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 $\frac{2}{11}$, and the number closest to 150 that is divisible by $11-143$. Therefore, the total number of samples in the container is 143. Samples of high-sulfur oil consist of all heavy oil samples ( $143: 11 \cdot 2=26$ ) and part 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 143:11.9=117. Among them, samples of low-sulfur oil constitute $\frac{7}{13}$ of the total, which is 77. Therefore, the number of high-sulfur light oil samples is 40. Then the total number of high-sulfur oil samples is: $26+40=66$.

Answer. 66.