Daily Math Puzzle: 2026-09-21

0.1792 — To calculate the probability that Team Velocity wins the championship given Team Dynamo won the first game, we need to consider the remaining games. The series is best-of-5, meaning the first team to win 3 games is crowned champion. Given: Team Dynamo (D) won Game 1. So, the current score is D:V = 1:0. Now, for Team Velocity (V) to win the championship, they must achieve 3 wins before Dynamo achieves 2 more wins (which would give Dynamo 3 wins in total). There are at most 4 more games to be played (Games 2, 3, 4, 5). P(Dynamo wins a game) = 0.6 P(Velocity wins a game) = 0.4 Velocity can win the championship in two ways, given Dynamo won Game 1: **Scenario 1: Velocity wins the championship in 4 total games (score D:V = 1:3).** This means Velocity must win Games 2, 3, and 4 consecutively. The sequence of wins would be D V V V. Since we are given that D won G1, we calculate the probability of V winning G2, G3, and G4: P(V wins G2, G3, G4) = P(V wins G2) * P(V wins G3) * P(V wins G4) = 0.4 * 0.4 * 0.4 = (0.4)^3 = 0.064. **Scenario 2: Velocity wins the championship in 5 total games (score D:V = 2:3).** This means Velocity must win Game 5, and in Games 2, 3, and 4, there must be 2 wins for Velocity and 1 win for Dynamo. If Velocity wins Game 5, it means the score after Game 4 was D:V = 2:2 (Dynamo having won G1 and one more, Velocity having won two games). First, let's find the probability that in Games 2, 3, and 4, Velocity wins 2 games and Dynamo wins 1 game: - The number of ways for this to happen is C(3,2) (choose which 2 games Velocity wins out of 3) = 3. - Each specific sequence (e.g., VVD, VDV, DVV) has a probability of (0.4)^2 * (0.6)^1 = 0.16 * 0.6 = 0.096. - So, the total probability of Velocity winning 2 and Dynamo winning 1 in Games 2, 3, 4 is 3 * 0.096 = 0.288. Then, Velocity must win Game 5 to secure the championship: P(V wins G5) = 0.4. So, the probability for Scenario 2 is P(2V, 1D in G2-4) * P(V wins G5) = 0.288 * 0.4 = 0.1152. **Total Probability:** Adding the probabilities from both scenarios gives the total probability that Velocity wins the championship, given Dynamo won the first game: P(Velocity wins | Dynamo won G1) = P(Scenario 1) + P(Scenario 2) = 0.064 + 0.1152 = 0.1792. The final answer is **0.1792**.