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There are three routes I can take to get from school to home. Every day when...

There are three routes I can take to get from school to home. Every day when I leave, I randomly select which route I will take (i.e. I am equally likely to take each of the three routes). Route 1 takes 3 minutes, Route 2 takes 5 minutes, and Route 3 takes 7 minutes. (a) What is the expected time it will take me to get home? (b) What is the variance of the time it will take me to get home? (c) Today there are roadblocks on two of the routes, but I don’t know which ones. I also don’t know my way around very well, so if I hit a roadblock I have to travel all the way back to school and start over. What is the expected time it will take me to get home now?

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