Subjects probability

Patrol Section C Aa3C76

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1. **Stating the problem:** We have four patrol teams starting from Station A at 09:00 and returning by 12:00, patrolling roads connecting six police stations (A, B, C, D, E, F). We want to find the probability that two patrol teams will pass through Section C. 2. **Understanding the constraints:** - Each road takes 30 minutes to cross. - No road is crossed by more than one team in the same direction at the same time. - Teams 2 and 3 are only in Sections E and D respectively at 10:00. - Teams 1 and 3 are only in Section E at 10:30. - Teams 1 and 4 are only in Sections B and E respectively at 11:30. - Teams 1 and 4 are the only ones patrolling the road connecting Sections A and E. - Team 4 never goes through Divisions B, D, or F. 3. **Analyzing team routes and constraints:** - Since Team 4 never goes through B, D, or F, and is on road A-E at 11:30, Team 4's route is limited to A, E, and possibly C. - Teams 2 and 3 are in E and D at 10:00, so they do not pass through C at that time. - Teams 1 and 3 are in E at 10:30, so Team 1 might pass through C before or after. - Teams 1 and 4 are in B and E at 11:30, so Team 1 is in B, Team 4 in E. 4. **Considering Section C:** - Team 4 can pass through C (since it avoids B, D, F). - Team 1 can pass through C to reach B or E. - Teams 2 and 3 do not pass through C based on their locations at 10:00 and 10:30. 5. **Conclusion:** - Only Teams 1 and 4 can pass through Section C. - The probability that two patrol teams pass through Section C is the probability that both Teams 1 and 4 pass through C. 6. **Since Teams 1 and 4 are the only ones who can pass through C, and both can do so, the probability is 1 (certainty) that two teams pass through Section C.**