# Relationship between events

#### jessxx

##### New Member
I've come across this exercise. There has been a research on free time activities, which has the following findings: 55% of people that are under 50 years old run regularly (three times per week), whereas only 35% of people who are over 50 run regularly. Assume that 60% of people are under 50 years old.
So the first question was, what is the probability that the person selected randomly will be running regulary. So that I believe is 47%.

Then the second question was "Two events in the previous example are running regularly and being over 50. How can we describe these two events? I would guess that these two events are non-mutually exclusive and independent but I am not sure. Can someone help me?

#### Dason

What does it mean for two events to be independent?

#### jessxx

##### New Member
I know that for non-independent events, the outcome of one event has an effect on the probability of another event occurring.
But on the other hand, being over 50 doesn't influence the fact that you run regularly or not. You can still be under 50 and exercise.

#### Dason

But on the other hand, being over 50 doesn't influence the fact that you run regularly or not. You can still be under 50 and exercise.
But what do the probabilities say? If the events are independent then the probability of running regularly will be the same for both groups.

#### jessxx

##### New Member
But what do the probabilities say? If the events are independent then the probability of running regularly will be the same for both groups.
Yeah they are not the same, so the events are then non-independent and non-mutually exclusive?