The Experts and the TV Viewers are playing "What? Where? When?" up to six wins - whoever wins six rounds first is the winner of the game. The probability of the Experts winning a 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.
To win, the Experts must win three rounds in a row (the probability of this is $0.6^{3}$) or lose exactly one of the next three rounds and win the $11$-th round (the probability of this is $3 \cdot 0.6^{2} \cdot 0.4 \cdot 0.6=3 \cdot 0.6^{3} \cdot 0.4$).

Therefore, the probability of the Experts winning is $0.6^{3}+3 \cdot 0.6^{3} \cdot 0.4=0.4752$.

## Answer

$0.4752$.

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