9. Solution. Suppose Olga Pavlovna has \( x \) liters of jam left, and Maria Petrovna has \( y \) liters of jam left. The numbers \( x \) and \( y \) are randomly and independently chosen from the interval from 0 to 1. We will consider that a random point with coordinates \((x; y)\) is selected from the unit square \( F \) (see the figure). The event \( A \) "the total amount of jam left with OP and MP is at least 1 liter but less than 1.5 liters" is expressed by the inequality \( 1 \leq x + y < 1.5 \) and is represented by a trapezoid enclosed between the lines \( x + y = 1 \) and \( x + y = 1.5 \). Then

\[
\mathrm{P}(A)=\frac{S_{A}}{S_{F}}=\frac{3}{8}=0.375
\]

![](https://cdn.mathpix.com/cropped/2024_05_06_df127e3cda0164ad6e6bg-2.jpg?height=606&width=606&top_left_y=1416&top_left_x=1319)
Answer: 0.375.

Note. Other solution methods are possible.

## Grading Criteria

| Solution is complete and correct | 3 points |
| :--- | :--- |
| The solution contains correct reasoning for individual cases and an enumeration of these cases, and the formula for total probability is applied to them. However, the answer may be incorrect | 1 point |
| The solution is incorrect or missing | 0 points |

## Variant 2