Definition
Dependent events
Events where one outcome changes the probability of another event.
Continue from this idea into connected AXIO math.
Change the group, change the chance.
Boundary: Dependence is about probabilities changing. It does not require one event to physically cause the other.
What it means
After the first event, ask whether the chances for the next event stay the same. If the chances change, the events are dependent. Sampling without replacement often does this because the group of possible outcomes changes.
Remember it
Change the group, change the chance.
Example
A bag has 3 red and 2 blue marbles. The chance of red first is 3/5. After drawing a red marble without replacement, the chance of red next is 2/4. Because the chance changed, the events are dependent.
Watch for
Dependence is about probabilities changing. It does not require one event to physically cause the other.
Common mix-up
With replacement, the bag returns to its original contents, so repeated draws can be independent instead.
Exact meaning
Dependent events are events for which knowing that one event occurred changes the probability of another event.