3 Reliability Questions

1. A subway train schedule for weekdays indicates that trains are supposed to arrive 10 minutes during the morning commute beginning at 6am and the last train is scheduled at 8am.

1. Determine the train schedule that should be posted.
2. Suppose that the reliability of these trains needs to be at least 90%. How many of the trains can be late in order to keep this system 90% reliable?

2. A product has 3 components with reliabilities of 0.9, 0.99, and 0.999. Determine the likelihood that it will fail.

3. A sports team needs two positions (A & B) that, without, they will have to forfeit. The reliability of each of the starters in these two positions are A = 0.95 and B = 0.9. Each of these positions does have a backup player just in case something should happen to the starter. The reliability of each back-up player is as follows: As Backup = 0.8 and Bs Backup = 0.85. If the reliability of the rest of the players is essentially inconsequential, what is the likelihood of forfeiting?

Please include work