Answer to question 9

The outcomes are all the different ways we can draw a ticket from G and another from F.  Let's represent a pair using parentheses.  For instance, if we draw "light" from G and "green" from F, ("light", "green") represents that pair.

The outcomes then are all possible combinations, which are

("light", "red"), ("light", "green"), ("light", "blue");
("dark", "red"), ("dark", "green"), ("dark", "blue).

Each combination is equally likely to occur, so we can represent G # F with six tickets, one different pair of outcomes on each ticket.  Their probabilities are therefore all equal to 1/6.

F # G looks just like G # F, except we reverse the order of each pair of outcomes on each ticket: ("light", "red") becomes ("red", "light"), and so on.  This is a technicality--F # G is not exactly the same as G # F--but obviously they are very closely related and provide the same information about the pair of boxes F and G.