3) A Game of Bridge You'll analyse a bridge-crossing game. Various scenarios will be considered. In each scenario, the game is as follows. All players begin at one end of the bridge, with the goal of getting all the way to the other side. The bridge consists of glass panes, each of which will turn red or green when stepped on. If a player stops on a pane and it turns red, that player is out. All lit panes remain lit for the entirety of the game (so later players have an advantage). Players will cross the bridge one at a time, in a predetermined order. You may also assume that the glass panes are large enough that players may not jump over segments of the bridge. That is, in the picture below, the players begin from the left side of the bridge and each player must step on one of the two panes in each column in an attempt to reach the right hand side of the bridge. Analyse the game by finding the expected number of players reaching the opposite end of the bridge safely (without stepping on a red glass pane) in each of the following scenarios. i) The bridge contains 2 glass panes in each segment and there are 18 segments to cross the entire bridge. That is, the bridge is like the one in the image above, but it contains 18 columns rather than just four. Each segment contains one pane that will light green and one pane that will light red. ii) The bridge contains 3 glass panes in each segment and there are 18 segments to cross the entire bridge. Each segment contains two panes that will light green and one pane that will light red. iii) The bridge contains 3 glass panes in each segment and there are 18 segments to cross the entire bridge. Each segment contains two panes that will light red and one that will light green. 3) A Game of Bridge You'll analyse a bridge-crossing game. Various scenarios will be considered. In each scenario, the game is as follows. All players begin at one end of the bridge, with the goal of getting all the way to the other side. The bridge consists of glass panes, each of which will turn red or green when stepped on. If a player stops on a pane and it turns red, that player is out. All lit panes remain lit for the entirety of the game (so later players have an advantage). Players will cross the bridge one at a time, in a predetermined order. You may also assume that the glass panes are large enough that players may not jump over segments of the bridge. That is, in the picture below, the players begin from the left side of the bridge and each player must step on one of the two panes in each column in an attempt to reach the right hand side of the bridge. Analyse the game by finding the expected number of players reaching the opposite end of the bridge safely (without stepping on a red glass pane) in each of the following scenarios. i) The bridge contains 2 glass panes in each segment and there are 18 segments to cross the entire bridge. That is, the bridge is like the one in the image above, but it contains 18 columns rather than just four. Each segment contains one pane that will light green and one pane that will light red. ii) The bridge contains 3 glass panes in each segment and there are 18 segments to cross the entire bridge. Each segment contains two panes that will light green and one pane that will light red. iii) The bridge contains 3 glass panes in each segment and there are 18 segments to cross the entire bridge. Each segment contains two panes that will light red and one that will light green