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.**
Patrol Section C Aa3C76
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.