[问答题]
After school, a group
(rnfsxf;i/0 br5ol i 9b*oim 2of six students play
1o+* 0q vny82(uxzmws /,ezr- fcfyera soccer passing game. Alex, Bella, Cleo, Dixie, and Emmy stand in a circle and pass the bal
u*rq-,(eyxms0v 1r f ez8oz2cf/n w+yl to each other while Ben, standing in the middle, tries to intercept the passes.
The following diagram shows the possible paths that the ball can be passed between the players, in the form of a directed graph. Some of the students are more likely to pass the ball to their friends than to other students. The paths shown by dotted lines represent a pass that is twice as likely as a pass shown by a solid line. For example, Dixie can pass the ball to Alex and Cleo with probability 0.25 and to Emmy with probability 0.5. Dixie won't pass the ball to Bella.
It is assumed that each player keeps the ball for a constant time before passing it. At the start of the game, Alex has the ball.
1. Determine the transition matrix for the graph.
2. Calculate the probability that Cleo has the ball after exactly four passes have been completed, assuming that Ben has not intercepted a pass.
3. If the players continue passing indefinitely, without an interception, determine which player will spend the least amount of time with the ball.
