statistics – Finding solutions to tutorial problems in probability

The set of tutorial problems

I’m taking a course in probability and statistics and wanted help with the solutions for the 3 problems (as part of my tutorial) attached (in the image). I couldn’t make much progress in 1 and 2 and for 3, I thought of the maximal cut algorithm but couldn’t write up a rigorous proof for the same. I’d greatly appreciate solutions to all the 3 tutorial problems

Thank you!