A box has 1 red marble and 7 white marbles. Two players (player I and player II) take turns drawing a marble from the box (without replacement). Let's denote the process as round 1, round 2, ...

Round 1: Player I draws a marble from the box (and keep it). If the marble is red, then play I wins and game over. If the marble is white, then go to round 2.

Round 2: player II draws a marble (and keep it). If the marble is red, then play II wins and game over. If the marble is white, then go to round 3.

Then keep going until someone draws the red marble.

1) List all the possible rounds that player I can win. List all the possible rounds that player II can win. (You just need to interpret the game and understand the rules to answer this question. No calculation required).

For question 2, 3, 4 and 5, you must explain how can player I or player II win. Giving the answer only will lead to no credit or little credit. For example, you must explain the process of the game such as "in round 1, player ..., then in round 2, player...".

2) What is the probability that player I wins in his/her first draw (This means it is round 1)? Make sure you have some explanation for your answer.

3) What is the probability that player II wins in his/her first draw (This means it is round 2)?

4) What is the probability that player I wins in his/her second draw (This means it is round 3)?

5) What is the probability that player II wins in his/her second draw (This means it is round 4)?

6) If you are playing this game, do you want to be player I or player II? Please explain your choice with probability.