9. Mini-tournament (recommended from 7th grade, 1 point). Alyosha, Borya, and Vasya are holding a mini-tournament in tennis: each plays with each other once. The winner gets 1 point, the loser gets 0, and there are no draws in tennis. The absolute winner of the mini-tournament is the one who has a total of 2 points. It is known that Alyosha wins against Borya with a probability of 0.6, and Borya wins against Vasya with a probability of 0.4. What is the probability of the event $C$ "there will be no absolute winner"?
Solution. Let the event “$X$ won against $Y$” be denoted as $X \square Y$. The event “no winner” will occur only if everyone has one point. This can happen in two cases:

$$
A \square B \square B \square A \text { and } B \square \delta \square A \square B .
$$

Let the unknown probability of the event $B \square A$ be denoted as $x$. Then

$$
\mathrm{P}(C)=\mathrm{P}(A \square K \square B \square A)+\mathrm{P}(B \square \delta \square A \square B)=0.6 \cdot 0.4 \cdot x+(1-0.4)(1-0.6)(1-x)=0.24
$$

Answer: 0.24.