Task 3. (15 points) Laboratory engineer Sergei received an object for research consisting of about 200 monoliths (a container designed for 200 monoliths, which was almost completely filled). Each monolith has a specific name (sandy loam or clayey loam) and genesis (marine or lake-glacial deposits). The relative frequency (statistical probability) that a randomly selected monolith will be sandy loam is $\frac{1}{9}$. The relative frequency that a randomly selected
monolith will be marine clayey loam is $\frac{11}{18}$. How many monoliths of lake-glacial genesis does the object contain, if there are no marine sandy loams among the sandy loams?
# Solution.

Let's determine the exact number of monoliths. It is known that the probability of a monolith being loamy sand is $\frac{1}{9}$. The number closest to 200 that is divisible by 9 is 198. Therefore, there are 198 monoliths in total. Monoliths of lacustrine-glacial origin consist of all loamy sands $(198: 9=22)$ and part of the clay loams. Let's find out how many monoliths of lacustrine-glacial origin are among the clay loams: The total number of clay loams is 198:9$\cdot$8=176. Among them, marine clay loams constitute $\frac{11}{18}$ of the total, which is 121. Therefore, the number of clay loams of lacustrine-glacial origin is 55. Thus, the total number of monoliths of lacustrine-glacial origin is: $22+55=77$.

Answer. 77.