# Calculate risk of unrelated groups

Let's say we have a few variables (made up numbers). Each percentage is a risk of failure later in life.

• Male 10%
• Woman 20%

• 25 years: 2%
• 50 years: 5%
• 70 years: 7%

### Interests

• Fotball: 10%
• Baseball: 40%
• Golf: 60%

## Question

How can I calculate the risk of for example a male that is 25 years old interested in golf?

## What I thought of so far - That did not work

1. First I thought I could make an avarage right across the board. But then I figured that inside the percentage on for example 50 years, genders is already accounted for. The groups gender, age and interests are self contained groups unaware of each other.
2. One person can have multiple interests which also mess up my thoughts.

How should I think around this case? I'm not a math experts so in case you add formulas, also add the thought process behind it.

• Important point: you need to know if all the "events" are independent. For example, are the events "male" and "football" independent? If not, it could be that only men like football! (because the percentages are the same) Mar 12 '20 at 13:28
• @MattiP. In the interests group there are fotball, baseball and golf. In this group there can be both male and female and the group does not know (or not care) about the gender within this group. Mar 12 '20 at 13:32
• So the percentages are to be interpreted like this: If you like golf, there's a 60% chance that you will fail at some point", right? Mar 12 '20 at 13:38
• @MattiP.Yes, that is correct. Mar 12 '20 at 13:39
• That's some really odd logic here ... So as with any probability question, I would start making shorthand notations. Let $P(X)=\text{probability that the person will fail at some point}$. Now the probabilities listed are something like $$P(X| \text{male}) = 0.1 \qquad P(X| \text{female}) = 0.2$$ Mar 12 '20 at 13:43