Hi, I'm a little confused by the concept of this Question. It is as follows:
you are told that a particular team has won w games, drawn d games and lost l games during the course of a season. Calculate the probability that (a) the team won both the first and the last games of the season, (b) the team lost both the first and the last games of the season.
for (a) I got the answer as this would be the multiplication of two independent events P(win)
First of all to notice at this point is the wording of the question,'calculate the probability', clearly I didn't get a numerical answer but an algebraic one. Assuming my answer is correct then this point is merely pettiness on my part however if my answer is incorrect, presuming there is a numerical solution then I would much appreciate any further insight anybody has!!!,,,
Secondly I have further constructive criticism of my answer. On the basis that since the first game not only has the number of total games (w+d+l)reduced by one altering in theory the denominator in my equation to w+d+l-1 but also the numerator(which I am not sure about) to 1,,,,,,as all the other w's would have been 'cancelled out' in the terms in the middle of the equation. In other words Im not sure as to whether the answer is not just the p(win)p(win) or p(win)p(draw)p(lose),,,,,,in some kind of order,,p(win) in which case considering the middle terms would involve some kind of algebraic permutation or combination as well as a confusing denominator and numerator for the w terms. The draw terms and lose terms contained in the middle though I am pretty sure the numerator for both draw and lose could be simplified into binomials of some sort.
As you can see I remain very confused as to how to solve this basic question and some insight and clarification of my thinking would be much appreciated. I just hope my first answer was correct. As for now I will continue to try obtain a solution to (b) thanks very much