10. Namesakes (recommended from 7th grade, 1 point) Let's assume that among eighth-graders, the name Alexander is three times more common than the name Alexandra, Yevgenyev is three times less common than Yevgeny, Valentinov is one and a half times more common than Valentin, and Vasilyev is 49 times more common than Vasilisa. One day, a randomly selected group of four eighth-graders, about whom we only know that they are called Sanya, Zhenya, Valya, and Vasya, drew lots. Find the probability that the lot was won by an eighth-grade girl, not an eighth-grade boy.

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# Solution.

$$
\frac{1}{4} \cdot \frac{1}{4}+\frac{1}{4} \cdot \frac{3}{4}+\frac{1}{4} \cdot \frac{2}{5}+\frac{1}{4} \cdot \frac{1}{50}=0.355
$$

Answer: 0.355 .