11. What? Where? When? Experts and Viewers play "What, Where, When" until six wins - whoever wins six rounds first is the winner. The probability of the Experts winning in one round is 0.6, and there are no ties. Currently, the Experts are losing with a score of $3: 4$. Find the probability that the Experts will still win.
Solution. Let the Experts win one round with probability $p$, and the Viewers with probability $q=1-p$.

The Experts need 3 more winning rounds to victory, while the Viewers need 2 more rounds. Thus, there can be no more than 4 rounds in total. Consider the possible chains of wins for the Experts (3) and the Viewers (V) in the next four rounds ${ }^{6}$. For example, the chain 33V3 leads to the Experts' victory with probability $p^{3} q$.

If a chain of four letters contains fewer than three letters 3, then it leads to the Viewers' victory.

In all other cases, that is, when the chain contains three or four letters 3, the Experts win. The probability of this is

$$
C_{4}^{4} p^{4}+C_{4}^{3} p^{3} q=1 \cdot 0.6^{4}+4 \cdot 0.6^{3} \cdot 0.4=0.4752
$$

Answer: 0.4752.