# Problem 6. (10 points)

Vasily is planning to graduate from college in a year. Only 270 out of 300 third-year students successfully pass their exams and complete their bachelor's degree. If Vasily ends up among the 30 expelled students, he will have to work with a monthly salary of 25,000 rubles. It is also known that every fifth graduate gets a job with a salary of 60,000 rubles per month, every tenth graduate earns 80,000 rubles per month, every twentieth graduate cannot find a job in their field and has an average salary of 25,000 rubles per month, while the salary of all others is 40,000 rubles. When Vasily finished school, he could have chosen not to go to college and instead work as a real estate assistant, like his friend Fyodor did. Fyodor's salary increases by 3,000 rubles each year. What is Vasily's expected salary? Whose salary will be higher in a year and by how much - Vasily's expected salary or Fyodor's actual salary, if Fyodor started working with a salary of 25,000 rubles at the same time Vasily enrolled in college? Note: Bachelor's degree education lasts 4 years.
# Solution:

In 4 years after graduating from school, Fedor will earn $25000 + 3000 * 4 = 37000$ rubles (2 points).

The expected salary of Vasily is the expected value of the salary Vasily can earn under all possible scenarios (2 points). It will be 270/300 * $(1 / 5 * 60000 + 1 / 10 * 80$ $000 + 1 / 20 * 25000 + (1 - 1 / 5 - 1 / 10 - 1 / 20) * 40000) + 30 / 300 * 25000 = 45025$ rubles (6 points).