How to calculate the probability of each goal in a match if the probability of one or more goals is 60%, and two or more goals is 25%?

Question

Mathematics

I guess the solution is:
60% - 25% = 35%.
And on average, 0.35 goals will be scored per match? I understand correctly? Or is it all wrong?
UPD: The probabilities of one or more and two or more goals are given. I need to calculate how many goals will be scored on average per match with an infinite number of matches. How to do it?

Answer 1

All wrong.
On average, 0.85 goals will be scored per match. Let's say we played 100 matches. Scored 60 first goals, 25 second. Only 85 out of 100.
PS Although, of course, the question remains about "two or more". After all, they can hammer five. So the correct answer is "from 0.85 goals and above on average per match."
PPS Based on the available information, you can build a probability function for each next goal scored. Build a series and find the limit. Will be cool :)

Answer 2

Given the probability pn that n or more goals will be scored.
Let the calculation accuracy be t=1/z, where z is a natural number.
Then at some step x: px=0 up to t. Or px<t, |p(x-1)>=t.
By definition of probability, the number of matches in the sample is z.
Then the number a(x-1) that will score x-1 goals is calculated as: a(x-1)=z*p(x-1).
The number x-2 is a(x-1)-z*a(x-2).
We iteratively obtain a sequence of the number of goals scored in a sample of matches.
Next, find the sum of this sequence and divide it by x.
We get the average number of goals scored.