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?

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

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