Analysis of Joint and Conditional Probability Outcomes

A bag contains \(10\) identical balls of which \(4\) are red and \(6\) are blue. Peter and Glen take turns to draw a ball from the bag without replacement. The first student to take a blue ball wins the game and the game ends.

1. Given that Peter takes the first draw, Glen takes the second draw, Peter then takes the third draw and so on, state, as a fraction, the probability that
   1. Peter wins at the first draw.
   2. Glen wins at the second draw.
   3. no fourth draw is required.
2. If the game ends at the \(n^{\mathrm{th}}\) draw, state the largest value of \(n\).