Suppose I have a table of soccer player salaries (in terms of high/medium/low):
I also have a table of soccer player goals scored (again in terms of high/medium/low):
And suppose I have a third table showing a breakdown of soccer player salaries and goals:
Low Medium High
Low 70 52 20
Goals Medium 43 47 22
High 44 66 57
Now suppose I want to calculate the probability that if I pick a soccer player at random, what is the chance that I will pick one with a high salary who scores a lot of goals?
It would seem there are two ways of calculating this - one from the separate goals and salaries tables - find the chance of picking one with a high salary, and combine it what the probability of picking one who scores a lot of goals, or look at the combined table and calculate the probability from that table.
The trouble is, each method gives a different answer.
Is there a way of finding what the correct answer is?