I am studying for a discrete math exam tomorrow and this is one of the review questions. I am having trouble answering the question as of now. If you could provide guidance on how to solve one or more of the following parts of the question, I would be really appreciative!! Let me know if you need any other information!
Assume that a string of length 9 is a random permutation of letters {a, b, c, d, e, f, g, h, i}.
(a) What is the probability of event A: letter g comes before a ?
(b) What is the probability of event B: letter g comes after b and d ?
(c) What is the probability of event C: letters e and f are before b and d ?
(d) Choose an arbitrary pair of events from {A, B, C} above and determine if these two are independent or not.
For the first three, you can ignore all the letters except those referenced in the question. All permutations of the letters of interest are equally likely. Now you are down to few enough to count by hand if you don't have a better idea.
For the last, one choice of the pair makes it easy in light of my earlier paragraph.