1.) Two university students agree to meet for a studying session. They decide to meet at a coffee shop some time between 6PM and 7PM, but neither of them enjoy waiting. Thus, they agree to leave if they have waited for fifteen minutes, or at 7PM, whichever comes first.
If both students show up randomly between 6PM and 7PM, what is the probability they will meet?
2.) Two students sit down to play a game involving a die with ten sides. The first player rolls the die. On a roll of 1-3 they receive one point and roll again. On a roll of 4-6 they hand the die to the second player and get no points. The second player rolls. On a roll of 1-4 they receive one point and roll again. On a roll of 5-6 they hand the die back to the first player. The game ends when one player reaches 5 points.
Describe how you could use a simulation to determine whether you wanted to be the player going first or second.