Suppose we know that the probability of x goals in a given soccer game is:
$10$% when $x = 0$
$20$% when $x=1$
- $25$% when $x = 2$
- $45$% when $x >2$
Every week $45$ games are played, contestants will choose $8$ matches from these $45$ and are given the following:
A) if the selected $8$ matches all have exactly $2$ goals scored each then the contestant will win \$$50$k
B) If there is EXACTLY $8$ matches with $2$ goals in each game then the contestant will win \$$100$k (i.e. if there is $>8$ matches with $2$ goals each then this scenario will not be possible, but A might be if the contestant chose the correct $8$ games)
I am trying to find the probability of scenario A and B.
Perhaps I am missing something, but is this not a binomial with parameters $Bin(45, 0.25)$ i.e. in any given game we have a probability of $0.25$ of getting exactly two goals.
Then scenario B will be $P(X=8)$ and scenario A will be $P(X>8)$?
It seems a little too simple - any advice