Winning a game probability

Suppose you are tied $$1-1$$ with Bob. To win the game, you have win greater than or equal to $$5$$ rounds and win at least $$2$$ more rounds than your opponent. The probability of winning a round is $$40\%$$ and each round is independent. What is the probability of you winning the game?

This would be: $$\left[1-P(\text{winning less than 5 rounds}) \times P(\text{win at least 2 more rounds than your opponent}\right]$$

$$= \left[1-\sum_{i=0}^{3} \binom{3}{i} (0.4)^{i}(0.6)^{3-i} \right] \times \left[P(\text{win at least 2 more rounds than your opponent}) \right]$$

What would be the second term? Would you just calculate 1-complement?

• It is a mistake in the placing of brackets! – OmG Jan 16 at 6:52