Each match played by a football team is won by that team with probability 1/2, is a draw with probability 1/6, and is lost with probability 1/3, with the result of each match being independent of all other results. For each of the following random variables related to this say how they are distributed.
(i) The number of drawn matches in a season lasting 38 matches.
ii) The number of matches up to and including their first win.
iii) The number of matches following their first defeat up to and including their next win.
iv) The number of matches up to and including their second loss.
v) The number of matches up to and including their mth loss where m is a fixed positive
- The can either be binomial
If nither of the above than give the pmf.
I can not tell which distritbutions are which. Can someone please help me.