To find the probability that the Dragons win this best of five series against the Goldfish, we'll consider the possible outcomes: ### Round 2: Dragons vs. Goldfish (Best of 5 series) The Dragons have an 80% chance of winning any single game. To win the series, they must win 3 or 4 games out of 5. Let's calculate the probability of each scenario: 1. Dragons win in 3 games: \[ P(\text{Dragons win in 3 games}) = (0.80)^3 \] 2. Dragons win in 4 games: - This can happen in 4 different ways: WWLW, WLWW, LWW, and WWW. - The probability of each of these sequences is: \[ P(WWLW) = (0.80)^3 \times (0.20) \] (where W represents a win and L represents a loss) - We need to consider all possible combinations where Dragons win 3 out of 4 games. Now, let's calculate: \[ P(\text{Dragons win in 4 games}) = 4 \times (0.80)^3 \times (0.20) \] 3. Dragons win in 5 games: - This happens when Dragons win 3 games and then lose 2, which can occur in 3 different ways: WWWLL, WWLWL, and WLWWL. - The probability of each sequence is: \[ P(WWWLL) = (0.80)^3 \times (0.20)^2 \] \[ P(\text{Dragons win in 5 games}) = 3 \times (0.80)^3 \times (0.20)^2 \] Now, let's sum up these probabilities to find the overall probability of the Dragons winning the series: \[ P(\text{Dragons win series}) = P(\text{Dragons win in 3 games}) + P(\text{Dragons win in 4 games}) + P(\text{Dragons win in 5 games}) \] \[ P(\text{Dragons win series}) = (0.80)^3 + 4 \times (0.80)^3 \times (0.20) + 3 \times